Spatially varying element properties

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

ProductsAbaqus/StandardAbaqus/Explicit

Features tested

This section demonstrates the use of distributions to model spatially varying element properties.

Using distributions to define thicknesses, offsets, material orientations, and stiffness matrices for shell and membrane elements

Elements tested

  • S3R
  • STRI3
  • S4
  • S4R
  • S4R5
  • STRI65
  • S8R
  • S8R5
  • S9R5
  • SC6R
  • SC8R
  • SAX1
  • SAX2
  • SAXA
  • M3D3
  • M3D4
  • M3D4R
  • M3D6
  • M3D8
  • M3D8R
  • M3D9
  • M3D9R

Problem description

The analyses in this section demonstrate how distributions can be used to define spatially varying element properties in shells and membrane elements (the membrane tests apply only to Abaqus/Standard).

The geometry in each shell test is a flat plate modeled with either 9 quadrilateral shell elements or 18 triangular shell elements. In most test cases each shell element is assigned a different thickness, offset, and material orientation using distributions. In some cases both distributions and nodal thicknesses are used to define the shell thicknesses. A linear elastic orthotropic material is used in each case. All the test cases in this section were verified by creating equivalent reference models using multiple section assignments to define the shell thicknesses, offsets, and material properties. Some of these reference models are included.

The geometry in each membrane test is a flat plate modeled with either 9 quadrilateral membrane elements or 18 triangular membrane elements. In most test cases each membrane element is assigned a different thickness and material orientation using distributions. A linear elastic material is used in each case. Initial stresses are applied to the membrane elements in all tests. All the test cases in this section were verified by creating equivalent reference models using multiple section assignments to define the membrane thicknesses and material orientations.

Loading:

The multistep Abaqus/Standard analysis performed on each shell model consists of the following:

  • Step 1: A frequency analysis.

  • Step 2: A steady-state dynamic analysis with modal damping and nodal loads.

  • Step 3: A modal dynamic analysis with modal damping and nodal loads.

  • Step 4: A direct steady-state dynamic analysis with modal damping and nodal loads.

  • Step 5: A subspace projection steady-state dynamic analysis with nodal loads.

  • Step 6: A random response analysis with nodal loads.

  • Step 7: A response spectrum analysis.

  • Step 8: A geometrically nonlinear static analysis with displacement boundary conditions.

  • Step 9: A load case static analysis using distributed body loads, gravity loads, and centrifugal loads.

The membrane tests are identical to the shell tests except that an initial static step is included to resolve the initial stresses.

A single geometrically nonlinear dynamic step with displacement boundary conditions is used for the shell models testing Abaqus/Explicit.

Results and discussion

The results for each model agree with the associated reference solutions.

Input files

Abaqus/Standard analyses

distrib_multistep_s3r_gs_std.inp

Multistep analysis using S3R elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s3r_nt_gs_std.inp

Multistep analysis using S3R elements, a homogeneous general shell section definition, and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_s3r_std.inp

Multistep analysis using S3R elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s3r_nt_std.inp

Multistep analysis using S3R elements with a homogeneous shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_s4_gs_std.inp

Multistep analysis using S4 elements and a homogeneous general shell section. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4_gs_ref_std.inp

Reference solution for distrib_multistep_s4_gs_std.inp using multiple homogeneous shell section definitions to define varying shell thicknesses, offsets, and material orientations.

distrib_multistep_s4_nt_gs_std.inp

Multistep analysis using S4 elements, a homogeneous general shell section definition, and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_s4_std.inp

Multistep analysis using S4 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4_rs_std.inp

Restart analysis for distrib_multistep_s4_std.inp.

distrib_multistep_s4_nt_std.inp

Multistep analysis using S4 elements with a homogeneous shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_s4_nt_ref_std.inp

Reference solution for distrib_multistep_s4_nt_std.inp using multiple homogeneous shell section definitions and nodal thicknesses to define varying shell thicknesses, offsets, and material orientations.

distrib_multistep_s4_nt1_gs_std.inp

Multistep analysis using S4 elements, a homogeneous general shell section definition, and nodal thicknesses. Distributions are used to define offsets and material orientations.

distrib_multistep_s4_nt1_std.inp

Multistep analysis using S4 elements with a homogeneous shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define offsets and material orientations.

distrib_multistep_s4_st_std.inp

Multistep analysis using S4 elements with a homogeneous general shell section definition. The section stiffness is specified directly. Distributions are used to define shell section stiffness and material orientations. The distributions for the section stiffnesses and material orientations are read from separate input files distrib_s4_stiff_in.inp and distrib_s4_orient_in.inp.

distrib_s4_stiff_in.inp

Input file for section stiffness distribution for distrib_multistep_s4_st_std.inp.

distrib_s4_orient_in.inp

Input file for material orientation distribution for distrib_multistep_s4_st_std.inp.

distrib_multistep_s4r_gs_std.inp

Multistep analysis using S4R elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4r_std.inp

Multistep analysis using S4R elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4r_hyp_std.inp

Multistep analysis using S4R elements with a homogeneous shell section definition that is integrated during the analysis and a hyperelastic material. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4r5_gs_std.inp

Multistep analysis using S4R5 elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s4r5_std.inp

Multistep analysis using S4R5 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s8r_gs_std.inp

Multistep analysis using S8R elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s8r_std.inp

Multistep analysis using S8R elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s8r5_gs_std.inp

Multistep analysis using S8R5 elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s8r5_std.inp

Multistep analysis using S8R5 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s9r5_gs_std.inp

Multistep analysis using S9R5 elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_s9r5_std.inp

Multistep analysis using S9R5 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_sc6r_gs_std.inp

Multistep analysis using SC6R elements and a homogeneous general shell section definition. Distributions are used to define material orientations.

distrib_multistep_sc6r_std.inp

Multistep analysis using SC6R elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define material orientations.

distrib_multistep_sc8r_gs_std.inp

Multistep analysis using SC8R elements and a homogeneous general shell section definition. Distributions are used to define material orientations.

distrib_multistep_sc8r_std.inp

Multistep analysis using SC8R elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define material orientations.

distrib_multistep_stri3_gs_std.inp

Multistep analysis using STRI3 elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_stri3_std.inp

Multistep analysis using STRI3 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_stri65_gs_std.inp

Multistep analysis using STRI65 elements and a homogeneous general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_stri65_std.inp

Multistep analysis using STRI65 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_sax1_std.inp

Multistep analysis using SAX1 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses and offsets.

distrib_multistep_sax2_std.inp

Multistep analysis using SAX2 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses and offsets.

distrib_multistep_sax2t_std.inp

Multistep analysis using SAX2T elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses and offsets.

distrib_multistep_saxa12_std.inp

Multistep analysis using SAXA12 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_saxa22_std.inp

Multistep analysis using SAXA22 elements with a homogeneous shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s3r_gs_std.inp

Multistep analysis using S3R elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s3r_nt_gs_std.inp

Multistep analysis using S3R elements, a composite general shell section definition, and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_comp_s3r_std.inp

Multistep analysis using S3R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s3r_nt_std.inp

Multistep analysis using S3R elements with a composite shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_comp_s3r_1_std.inp

Multistep analysis using S3R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4_gs_std.inp

Multistep analysis using S4 elements and a composite general shell section. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4_gs_ref_std.inp

Reference solution for distrib_multistep_comp_s4_gs_std.inp using multiple composite shell section definitions to define varying shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4_nt_gs_std.inp

Multistep analysis using S4 elements, a composite general shell section definition, and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_comp_s4_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4_rs_std.inp

Restart analysis for distrib_multistep_comp_s4_std.inp.

distrib_multistep_comp_s4_nt_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_multistep_comp_s4_nt_ref_std.inp

Reference solution for distrib_multistep_comp_s4_nt_std.inp using multiple composite shell section definitions and nodal thicknesses to define varying shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4_nt1_gs_std.inp

Multistep analysis using S4 elements, a composite general shell section definition, and nodal thicknesses. Distributions are used to define offsets and material orientations.

distrib_multistep_comp_s4_nt1_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define offsets and material orientations.

distrib_multistep_comp_s4_3_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4_4_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4_5_std.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4r_gs_std.inp

Multistep analysis using S4R elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4_gs_3_std.inp

Multistep analysis using S4 elements with a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4_gs_4_std.inp

Multistep analysis using S4 elements with a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4_gs_5_std.inp

Multistep analysis using S4 elements with a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s4r_std.inp

Multistep analysis using S4R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4r_hyp_std.inp

Multistep analysis using S4R elements with a composite shell section definition that is integrated during the analysis and a hyperelastic material. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4r5_gs_std.inp

Multistep analysis using S4R5 elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s4r5_std.inp

Multistep analysis using S4R5 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s8r_gs_std.inp

Multistep analysis using S8R elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s8r_std.inp

Multistep analysis using S8R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s8r5_gs_std.inp

Multistep analysis using S8R5 elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s8r5_std.inp

Multistep analysis using S8R5 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_s9r5_gs_std.inp

Multistep analysis using S9R5 elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_s9r5_std.inp

Multistep analysis using S9R5 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_sc6r_gs_std.inp

Multistep analysis using SC6R elements and a composite general shell section definition. Distributions are used to define material orientations.

distrib_multistep_comp_sc6r_std.inp

Multistep analysis using SC6R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define material orientations.

distrib_multistep_comp_sc8r_gs_std.inp

Multistep analysis using SC8R elements and a composite general shell section definition. Distributions are used to define material orientations.

distrib_multistep_comp_sc8r_std.inp

Multistep analysis using SC8R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define material orientations.

distrib_multistep_comp_sc8r_1_std.inp

Multistep analysis using SC8R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_sc8r_2_std.inp

Multistep analysis using SC8R elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_sc8r_gs_1_std.inp

Multistep analysis using SC8R elements with a composite general shell section definition. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_sc8r_gs_2_std.inp

Multistep analysis using SC8R elements with a composite general shell section definition. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_stri3_gs_std.inp

Multistep analysis using STRI3 elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_stri3_std.inp

Multistep analysis using STRI3 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_comp_stri65_gs_std.inp

Multistep analysis using STRI65 elements and a composite general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_stri65_std.inp

Multistep analysis using STRI65 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_saxa12_std.inp

Multistep analysis using SAXA12 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

distrib_multistep_comp_saxa22_std.inp

Multistep analysis using SAXA22 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, material orientations, composite layer thicknesses, and composite layer angles.

distrib_multistep_m3d3_std.inp

Multistep analysis using M3D3 elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d4_std.inp

Multistep analysis using M3D4 elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d4r_std.inp

Multistep analysis using M3D4R elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d6_std.inp

Multistep analysis using M3D6 elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d8_std.inp

Multistep analysis using M3D8 elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d8r_std.inp

Multistep analysis using M3D8R elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d9_std.inp

Multistep analysis using M3D9 elements. Distributions are used to define membrane thicknesses and material orientations.

distrib_multistep_m3d9r_std.inp

Multistep analysis using M3D9R elements. Distributions are used to define membrane thicknesses and material orientations.

Abaqus/Explicit analyses

distrib_s4_nt_xpl.inp

Analysis using S4 elements with a shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_s4_nt_ref_xpl.inp

Reference solution for distrib_s4_nt_xpl.inp using multiple shell section definitions and nodal thicknesses to define varying shell thicknesses and material orientations.

distrib_s4r_nt_xpl.inp

Analysis using S4R elements with a shell section definition that is integrated during the analysis and nodal thicknesses. Distributions are used to define shell thicknesses and material orientations.

distrib_s4r_nt_ref_xpl.inp

Reference solution for distrib_s4r_nt_xpl.inp using multiple shell section definitions and nodal thicknesses to define varying shell thicknesses and material orientations.

distrib_comp_s4_nt_xpl.inp

Multistep analysis using S4 elements with a composite shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses and material orientations.

distrib_comp_s4_nt_ref_xpl.inp

Reference solution for distrib_comp_s4_nt_xpl.inp using multiple composite shell section definitions and nodal thicknesses to define varying shell thicknesses and material orientations.

distrib_comp_s3r_angle_xpl.inp

Analysis using S3R elements with composite shell section definitions that are integrated during the analysis. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s3r_angle_ref_xpl.inp

Reference solution for distrib_comp_s3r_angle_xpl.inp using multiple composite shell section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4_angle_xpl.inp

Analysis using S4 elements with composite shell section definitions that are integrated during the analysis. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4_angle_ref_xpl.inp

Reference solution for distrib_comp_s4_angle_xpl.inp using multiple composite shell section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4r_angle_xpl.inp

Analysis using S4R elements with composite shell section definitions that are integrated during the analysis. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4r_angle_ref_xpl.inp

Reference solution for distrib_comp_s4r_angle_xpl.inp using multiple composite shell section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4rs_angle_xpl.inp

Analysis using S4RS elements with composite shell section definitions that are integrated during the analysis. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4rs_angle_ref_xpl.inp

Reference solution for distrib_comp_s4rs_angle_xpl.inp using multiple composite shell section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s3r_gs_angle_xpl.inp

Analysis using S3R elements with composite general shell section definitions. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s3r_gs_angle_ref_xpl.inp

Reference solution for distrib_comp_s3r_gs_angle_xpl.inp using multiple composite shell general section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4_gs_angle_xpl.inp

Analysis using S4 elements with composite general shell section definitions. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4_gs_angle_ref_xpl.inp

Reference solution for distrib_comp_s4_gs_angle_xpl.inp using multiple composite shell general section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4r_gs_angle_xpl.inp

Analysis using S4R elements with composite general shell section definitions. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4r_gs_angle_ref_xpl.inp

Reference solution for distrib_comp_s4r_gs_angle_xpl.inp using multiple composite shell general section definitions to define varying composite layer angles and thicknesses.

distrib_comp_s4rs_gs_angle_xpl.inp

Analysis using S4RS elements with composite general shell section definitions. Distributions are used to define composite layer angles and thicknesses.

distrib_comp_s4rs_gs_angle_ref_xpl.inp

Reference solution for distrib_comp_s4rs_gs_angle_xpl.inp using multiple composite shell general section definitions to define varying composite layer angles and thicknesses.

distrib_s3r_gs_stiff_xpl.inp

Analysis using S3R elements with homogeneous general shell section definitions and direct section stiffness specification. Distributions are used to define shell section stiffness.

distrib_s3r_gs_stiff_ref_xpl.inp

Reference solution for distrib_s3r_gs_stiff_xpl.inp using multiple homogeneous general shell section definitions to define varying shell section stiffness.

distrib_s4_gs_stiff_xpl.inp

Analysis using S4 elements with homogeneous general shell section definitions and direct section stiffness specification. Distributions are used to define shell section stiffness.

distrib_s4_gs_stiff_ref_xpl.inp

Reference solution for distrib_s4_gs_stiff_xpl.inp using multiple homogeneous general shell section definitions to define varying shell section stiffness.

distrib_s4r_gs_stiff_xpl.inp

Analysis using S4R elements with homogeneous general shell section definitions and direct section stiffness specification. Distributions are used to define shell section stiffness.

distrib_s4r_gs_stiff_ref_xpl.inp

Reference solution for distrib_s4r_gs_stiff_xpl.inp using multiple homogeneous general shell section definitions to define varying shell section stiffness.

distrib_s4rs_gs_stiff_xpl.inp

Analysis using S4RS elements with homogeneous general shell section definitions and direct section stiffness specification. Distributions are used to define shell section stiffness.

distrib_s4rs_gs_stiff_ref_xpl.inp

Reference solution for distrib_s4rs_gs_stiff_xpl.inp using multiple homogeneous general shell section definitions to define varying shell section stiffness.

Using distributions to define material orientations and material behaviors for continuum elements

Elements tested

  • CPS3
  • CPE3
  • CPS4
  • CPS4R
  • CPE4
  • CPE4H
  • CPE4I
  • CPE4R
  • CPS6
  • CPS6M
  • CPE6
  • CPE6M
  • CPS8
  • CPS8R
  • CPE8
  • CPE8R
  • CAX3
  • CAX4
  • CAX4H
  • CAX4I
  • CAX4R
  • CAX6
  • CAX6M
  • CAX8
  • CAX8R
  • CGAX3
  • CGAX4
  • CGAX4H
  • CGAX4R
  • CGAX6
  • CGAX6M
  • CGAX8
  • CGAX8R
  • C3D4
  • C3D6
  • C3D8
  • C3D10
  • C3D10HS
  • C3D10M
  • C3D15
  • C3D20
  • CCL12
  • CCL24
  • MAX1
  • MAX2
  • MCL6
  • MCL9
  • MGAX1
  • MGAX2
  • CSS8

Problem description

The analyses in this section demonstrate how distributions can be used to define material orientations and material behavior on an element-by-element basis for continuum elements. The geometry in two-dimensional tests is a unit square modeled with either 9 quadrilateral or 18 triangular elements. The geometry in the three-dimensional tests is a unit cube with between 8 to 12 elements. In most test cases each solid element is assigned a different material orientation using a distribution. In some of the test cases distributions of material behaviors are used. All the test cases in this section were verified by creating equivalent reference models using multiple section assignments to define material orientations. Some of these reference models are included. In some cases the residual mode functionality is also tested.

Some of the Abaqus/Standard tests include membrane elements with thicknesses and material orientations defined with distributions.

Loading:

The multistep Abaqus/Standard analysis performed on each model consists of the following:

  • Step 1: A frequency analysis.

  • Step 2: A steady-state dynamic analysis with modal damping and nodal loads.

  • Step 3: A modal dynamic analysis with modal damping and nodal loads.

  • Step 4: A direct steady-state dynamic analysis with modal damping and nodal loads.

  • Step 5: A subspace projection steady-state dynamic analysis with nodal loads.

  • Step 6: A random response analysis with nodal loads.

  • Step 7: A response spectrum analysis.

  • Step 8: A geometrically nonlinear static analysis with displacement boundary conditions.

  • Step 9: A load case static analysis using distributed body loads, gravity loads, and centrifugal loads.

For cases in which the residual mode functionality is tested, a static perturbation step is added prior to the frequency step.

Only the eighth step above is used for the models testing Abaqus/Explicit.

Results and discussion

The results for each model agree with the associated reference solutions.

Input files

Abaqus/Standard analyses

distrib_multistep_c3d4_std.inp

Multistep analysis using C3D4 elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_c3d6_std.inp

Multistep analysis using C3D6 elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_c3d8_std.inp

Multistep analysis using C3D8 elements. Distributions are used to define material orientations and orthotropic elastic behavior. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_c3d8_comp_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations.

distrib_multistep_comp_c3d8_1_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_c3d8_2_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_c3d8_3_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_c3d8_4_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_comp_c3d8_5_std.inp

Multistep analysis using composite C3D8 elements. Distributions are used to define material orientations and composite layer orientation angles.

distrib_multistep_c3d10_std.inp

Multistep analysis using C3D10 elements. Distributions are used to define material orientations, orthotropic elastic behavior, and material density.

distrib_multistep_c3d10hs_std.inp

Multistep analysis using C3D10HS elements. Distributions are used to define material orientations, orthotropic elastic behavior, and material density.

distrib_multistep_c3d10_ref_std.inp

Reference solution for distrib_multistep_c3d10_std.inp using multiple solid section and material definitions to define varying material orientations and material behavior.

distrib_multistep_c3d10hs_ref_std.inp

Reference solution for distrib_multistep_c3d10hs_std.inp using multiple solid section and material definitions to define varying material orientations and material behavior.

distrib_multistep_c3d10m_std.inp

Multistep analysis using C3D10M elements. Distributions are used to define material orientations and anisotropic elastic behavior. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_c3d15_std.inp

Multistep analysis using C3D15 elements. Distributions are used to define material orientations.

distrib_multistep_c3d20r_std.inp

Multistep analysis using C3D20R elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_c3d20r_comp1_std.inp

Multistep analysis using composite C3D20R elements. Distributions are used to define material orientations.

distrib_multistep_c3d20r_comp2_std.inp

Multistep analysis using composite C3D20R elements. Distributions are used to define material orientations.

distrib_multistep_ccl12_mcl6_std.inp

Multistep analysis using CCL12 and MCL6 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_ccl24_mcl9_std.inp

Multistep analysis using CCL24 and MCL9 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_cax3_std.inp

Multistep analysis using CAX3 elements. Distributions are used to define material orientations.

distrib_multistep_cax4_std.inp

Multistep analysis using CAX4 and MAX1 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_cax4h_std.inp

Multistep analysis using CAX4H elements. Distributions are used to define material orientations.

distrib_multistep_cax4i_std.inp

Multistep analysis using CAX4I elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_cax4r_std.inp

Multistep analysis using CAX4R elements. Distributions are used to define material orientations.

distrib_multistep_cax6_std.inp

Multistep analysis using CAX6 elements. Distributions are used to define material orientations.

distrib_multistep_cax6m_std.inp

Multistep analysis using CAX6M elements. Distributions are used to define material orientations.

distrib_multistep_cax8_std.inp

Multistep analysis using CAX8 and MAX2 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_cax8r_std.inp

Multistep analysis using CAX8R elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_cgax3_std.inp

Multistep analysis using CGAX3 elements. Distributions are used to define material orientations.

distrib_multistep_cgax4_std.inp

Multistep analysis using CGAX4 and MGAX1 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_cgax4h_std.inp

Multistep analysis using CGAX4H elements. Distributions are used to define material orientations.

distrib_multistep_cgax4r_std.inp

Multistep analysis using CGAX4R elements. Distributions are used to define material orientations.

distrib_multistep_cgax6_std.inp

Multistep analysis using CGAX6 elements. Distributions are used to define material orientations.

distrib_multistep_cgax8_std.inp

Multistep analysis using CGAX8 and MGAX2 elements. Distributions are used to define material orientations and membrane thicknesses.

distrib_multistep_cgax8r_std.inp

Multistep analysis using CGAX8R elements. Distributions are used to define material orientations.

distrib_multistep_cpe3_std.inp

Multistep analysis using CPE3 elements. Distributions are used to define material orientations.

distrib_multistep_cpe4_std.inp

Multistep analysis using CPE4 elements. Distributions are used to define material orientations.

distrib_multistep_cpe4h_std.inp

Multistep analysis using CPE4H elements. Distributions are used to define material orientations.

distrib_multistep_cpe4i_std.inp

Multistep analysis using CPE4I elements. Distributions are used to define material orientations.

distrib_multistep_cpe4r_std.inp

Multistep analysis using CPE4R elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_cpe6_std.inp

Multistep analysis using CPE6 elements. Distributions are used to define material orientations.

distrib_multistep_cpe6m_std.inp

Multistep analysis using CPE6M elements. Distributions are used to define material orientations.

distrib_multistep_cpe8_std.inp

Multistep analysis using CPE8 elements. Distributions are used to define material orientations, orthotropic elastic behavior (with engineering constants), and material density. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_cpe8_ref_std.inp

Reference solution for distrib_multistep_cpe8_std.inp using multiple solid section definitions to define varying material orientations.

distrib_multistep_cpe8r_std.inp

Multistep analysis using CPE8R elements. Distributions are used to define material orientations.

distrib_multistep_cps3_std.inp

Multistep analysis using CPS3 elements. Distributions are used to define material orientations.

distrib_multistep_cps4_std.inp

Multistep analysis using CPS4 elements. Distributions are used to define material orientations and lamina elastic behavior.

distrib_multistep_cps4r_std.inp

Multistep analysis using CPS4R elements. Distributions are used to define material orientations.

distrib_multistep_cps6_std.inp

Multistep analysis using CPS6 elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_cps6m_std.inp

Multistep analysis using CPS6M elements. Distributions are used to define material orientations.

distrib_multistep_cps8_std.inp

Multistep analysis using CPS8 elements. Distributions are used to define material orientations.

distrib_multistep_cps8r_std.inp

Multistep analysis using CPS8R elements. Distributions are used to define material orientations. In addition, residual modes are activated in the frequency step for use in the subsequent modal procedures.

distrib_multistep_css8_comp_std.inp

Multistep analysis using composite CSS8 elements. Distributions are used to define material orientations.

distrib_multistep_css8_comp_ref_std.inp

Reference solution for distrib_multistep_css8_comp_std.inp using multiple solid section definitions to define varying material orientations.

distrib_multistep_css8_std.inp

Multistep analysis using CSS8 elements. Distributions are used to define material orientations.

distrib_multistep_css8_ref_std.inp

Reference solution for distrib_multistep_css8_std.inp using multiple solid section definitions to define varying material orientations.

Abaqus/Explicit analyses

distrib_c3d10m_xpl.inp

Analysis using C3D10M elements. Distributions are used to define material orientations.

distrib_c3d10m_ref_xpl.inp

Reference solution for distrib_c3d10m_xpl.inp using multiple solid section definitions to define varying material orientations.

Using distributions while transferring results from one Abaqus/Standard analysis to another

Elements tested

  • S3R
  • S4R
  • SAX1
  • CPE4
  • CPS4
  • C3D8

Problem description

The analyses in this section demonstrate that element properties defined with distributions can be transferred from one Abaqus/Standard analysis to another. All the test cases in this section were verified by creating equivalent reference models using multiple section assignments to define the shell thicknesses, offsets, and material properties. Some of these reference models are included.

Results and discussion

The results for each model agree with the associated reference solutions.

Input files

ss1_c3d8_ep.inp

Two geometrically nonlinear static steps using C3D8 elements. Distributions are used to define material orientations and orthotropic elastic behavior (using engineering constants).

ss2_c3d8_ep_n_n.inp

Imports both elements in ss1_c3d8_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_ep_n_y.inp

Imports both elements in ss1_c3d8_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new C3D8 element is defined.

ss2_c3d8_ep_y_n.inp

Imports both elements in ss1_c3d8_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_ep_y_y.inp

Imports both elements in ss1_c3d8_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new C3D8 element is defined.

ss1_c3d8_1_ep.inp

Two geometrically nonlinear static steps using C3D8 elements. Distributions are used to define material orientations and orthotropic elastic behavior.

ss2_c3d8_1_ep_n_n.inp

Imports both elements in ss1_c3d8_1_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_1_ep_n_y.inp

Imports both elements in ss1_c3d8_1_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new C3D8 element is defined.

ss2_c3d8_1_ep_y_n.inp

Imports both elements in ss1_c3d8_1_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_1_ep_y_y.inp

Imports both elements in ss1_c3d8_1_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new C3D8 element is defined.

ss1_c3d8_2_ep.inp

Two geometrically nonlinear static steps using C3D8 elements. Distributions are used to define material orientations and anisotropic elastic behavior.

ss2_c3d8_2_ep_n_n.inp

Imports both elements in ss1_c3d8_2_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_2_ep_n_y.inp

Imports both elements in ss1_c3d8_2_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new C3D8 element is defined.

ss2_c3d8_2_ep_y_n.inp

Imports both elements in ss1_c3d8_2_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new C3D8 element is defined.

ss2_c3d8_2_ep_y_y.inp

Imports both elements in ss1_c3d8_2_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new C3D8 element is defined.

ss1_cpe4_ep.inp

Two geometrically nonlinear static steps using CPE4 elements. Distributions are used to define material orientations and isotropic elastic behavior.

ss2_cpe4_ep_n_n.inp

Imports both elements in ss1_cpe4_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new CPE4 element is defined.

ss2_cpe4_ep_n_y.inp

Imports both elements in ss1_cpe4_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new CPE4 element is defined.

ss2_cpe4_ep_y_n.inp

Imports both elements in ss1_cpe4_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new CPE4 element is defined.

ss2_cpe4_ep_y_y.inp

Imports both elements in ss1_cps4_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new CPE4 element is defined.

ss1_cps4_ep.inp

Two geometrically nonlinear static steps using CPS4 elements. Distributions are used to define material orientations and lamina elastic behavior.

ss2_cps4_ep_n_n.inp

Imports both elements in ss1_cps4_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new CPS4 element is defined.

ss2_cps4_ep_n_y.inp

Imports both elements in ss1_cps4_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new CPS4 element is defined.

ss2_cps4_ep_y_n.inp

Imports both elements in ss1_cps4_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new CPS4 element is defined.

ss2_cps4_ep_y_y.inp

Imports both elements in ss1_cps4_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new CPS4 element is defined.

ss1_s3r_ep.inp

Two geometrically nonlinear static steps using S3R elements with a shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

ss2_s3r_ep_n_n.inp

Imports both elements in ss1_s3r_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new S3R element is defined.

ss2_s3r_ep_n_y.inp

Imports both elements in ss1_s3r_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new S3R element is defined.

ss2_s3r_ep_y_n.inp

Imports both elements in ss1_s3r_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new S3R element is defined.

ss2_s3r_ep_y_y.inp

Imports both elements in ss1_s3r_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new S3R element is defined.

ss1_s4r_ep.inp

Two geometrically nonlinear static steps using S4R elements with a shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses, offsets, and material orientations.

ss2_s4r_ep_n_n.inp

Imports both elements in ss1_s4r_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_n_y.inp

Imports both elements in ss1_s4r_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new S4R element is defined.

ss2_s4r_ep_y_n.inp

Imports both elements in ss1_s4r_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_y_y.inp

Imports both elements in ss1_s4r_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new S4R element is defined.

ss1_s4r_ep_ref.inp

Reference solution for ss1_s4r_ep.inp using multiple shell section definitions to define varying shell thicknesses, offsets, and material orientations.

ss2_s4r_ep_ref_n_n.inp

Reference solution for ss2_s4r_ep_n_n.inp.

ss2_s4r_ep_ref_n_y.inp

Reference solution for ss2_s4r_ep_n_y.inp.

ss2_s4r_ep_ref_y_n.inp

Reference solution for ss2_s4r_ep_y_n.inp.

ss2_s4r_ep_ref_y_y.inp

Reference solution for ss2_s4r_ep_y_y.inp.

ss1_s4r_ep_gs.inp

Two geometrically nonlinear static steps using S4R elements with a general shell section definition. Distributions are used to define shell thicknesses, offsets, and material orientations.

ss2_s4r_ep_gs_n_n.inp

Imports both elements in ss1_s4r_ep_gs.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_gs_n_y.inp

Imports both elements in ss1_s4r_ep_gs.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new S4R element is defined.

ss2_s4r_ep_gs_y_n.inp

Imports both elements in ss1_s4r_ep_gs.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_gs_y_y.inp

Imports both elements in ss1_s4r_ep_gs.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new S4R element is defined.

ss1_s4r_ep_gs_st.inp

Two geometrically nonlinear static steps using S4R elements with a general shell section definition. The section stiffness is specified directly. Distributions are used to define shell section stiffness and material orientations.

ss2_s4r_ep_gs_st_n_n.inp

Imports both elements in ss1_s4r_ep_gs_st.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_gs_st_n_y.inp

Imports both elements in ss1_s4r_ep_gs_st.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new S4R element is defined.

ss2_s4r_ep_gs_st_y_n.inp

Imports both elements in ss1_s4r_ep_gs_st.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new S4R element is defined.

ss2_s4r_ep_gs_st_y_y.inp

Imports both elements in ss1_s4r_ep_gs_st.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new S4R element is defined.

ss1_sax1_ep.inp

Two geometrically nonlinear static steps using SAX1 elements with a shell section definition that is integrated during the analysis. Distributions are used to define shell thicknesses and offsets.

ss2_sax1_ep_n_n.inp

Imports both elements in ss1_sax1_ep.inp at the end of Step 1 with UPDATE=NO and STATE=NO. One new SAX1 element is defined.

ss2_sax1_ep_n_y.inp

Imports both elements in ss1_sax1_ep.inp at the end of Step 1 with UPDATE=NO and STATE=YES. One new SAX1 element is defined.

ss2_sax1_ep_y_n.inp

Imports both elements in ss1_sax1_ep.inp at the end of Step 1 with UPDATE=YES and STATE=NO. One new SAX1 element is defined.

ss2_sax1_ep_y_y.inp

Imports both elements in ss1_sax1_ep.inp at the end of Step 1 with UPDATE=YES and STATE=YES. One new SAX1 element is defined.

ss1_sax1_ep_ref.inp

Reference solution for ss1_sax1_ep.inp using multiple shell section definitions to define varying shell thicknesses and offsets.

ss2_sax1_ep_ref_n_n.inp

Reference solution for ss2_sax1_ep_n_n.inp.

ss2_sax1_ep_ref_n_y.inp

Reference solution for ss2_sax1_ep_n_y.inp.

ss2_sax1_ep_ref_y_n.inp

Reference solution for ss2_sax1_ep_y_n.inp.

ss2_sax1_ep_ref_y_y.inp

Reference solution for ss2_sax1_ep_y_y.inp.

Using distributions for specifying orientation for connector elements

Elements tested

  • CONN3D2

Problem description

The analyses in this section demonstrate the use of distributions for specifying orientation for connectors. Some of these reference models are included.

Results and discussion

The results for each model agree with the associated reference solutions.

Input files

distrib_ori_connect_1.inp

Several CONN3D2 elements with beam-type connector sections are used in this test. Distributions are used to define orientations at the two nodes for the connector elements. All degrees of freedom are fixed at node a of the connector elements, and the CLOAD option is applied at node b such that the connector total force CTF in component 1 is 1.0 units, the total force in component 2 is 2.0 units, and the total force in component 3 is 3.0 units.

distrib_ori_connect_1_xpl.inp

Several CONN3D2 elements with beam-type connector sections are used in this test. Distributions are used to define orientations at the two nodes for the connector elements. All degrees of freedom are fixed at node a of the connector elements, and the CLOAD option is applied quasi-statically at node b such that the connector total force CTF in component 1 is 1.0 units, the total force in component 2 is 2.0 units, and the total force in component 3 is 3.0 units.