Summary

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Two overlapping plates (aluminum) are connected by a rivet (titanium) forming a lap joint. The aluminum and titanium materials are both defined by piece-wise linear elasto-plastic law. The plates and the rivet are meshed with solid elements. The free end of the bottom plate is constrained and the free end of the top plate is pulled (by applying imposed displacement) to shear the joint. An all inclusive contact is defined such that all the components in the model are master and all nodes of the model are slave.

This example is considered a static problem and the nonlinear implicit solver is used.

 

Overview

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Aim of the Problem

The purpose of this example is to demonstrate a nonlinear large displacement implicit analysis (NLGEOM) involving elasto-plastic material and contact using OptiStruct.

Physical Problem Description

The top and bottom plates have a length of 30mm, width of 20mm and height of 1.5mm. The rivet is 8mm in diameter and 6mm in height. The geometry of the joint is shown in Figure 1. Due to symmetry only half of the joint is modeled.

 

Fig 1: Geometry of the joint.

The material used for the aluminum plates have the following properties:

The stress vs plastic strain plot for aluminum is shown in Figure 2.

Fig 2: Stress – plastic strain curve for aluminum

The material used for the titanium rivet has the following properties:

The stress vs plastic strain plot for titanium is shown in Figure 3.

Fig 3: Stress – plastic strain curve for titanium

Analysis, Assumptions and Modeling Description

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Geometric Linear (NLSTAT) or Geometric Nonlinear (NLGEOM) Analysis

In a geometric linear analysis all deformations and rotations are small – displacements of 5% of the model dimension are considered small.

For this lap joint example, the final deformations and strains after shearing of the lap joint are 9.5% of the largest dimension of the model (30mm). So, the geometrically nonlinear static NLSTAT analysis could not be considered for this example.

Modeling Methodology

The mesh is a regular solid mesh with the plates being around 1.5mm in dimension and the rivet being around 0.5mm in dimension.

The plates and rivet have been modeled using first order fully-integrated solid elements.

PSOLID          4       1

PSOLIDX        4      14     222             VAR

 

The boundary conditions applied in the model are shown in Figure 4.

Fig 4: Boundary conditions

The imposed displacements are defined in FEM file using NLOAD1 card:

 

SPCD           3     572  1     2.5    

………………

TABLED1        8  LINEAR  LINEAR

+            0.0     0.0     1.0     1.0ENDT  

NLOAD1         7       3            DISP       8

 

OptiStruct Options Used

An all inclusive general purpose contact has been defined in the model. All the nodes of the model are defined as slave and all components in the model are defined as the master.

SET     2       GRID    LIST  

+       1       2       3       4       5       6       7       8      

+       9       10      11      12      13      14      15      16

………………………………

SET     7       ELEM    PROP  

+       4       5       6  

 

CONTACT        6       7       2       7 OPENGAP  

 

A small physical gap of around 0.02mm has been introduced between the top and bottom plates and also between the plates and the rivet. The minimum gap specified (0.022) for the contact is slightly higher than the physical gap for contact to take effect. A static Coulomb friction of 0.05 is defined for the interface.

PCONT          7        AUTO  

PCONTX        7          0.05    0.022                  0

+                               CONST      

+                                             4

+

+           COUL   STIFF

+

 

The plasticity and contact causes major nonlinearities; therefore, a static nonlinear analysis is performed using the arc-length displacement strategy. The time step is determined by a displacement norm control.

The nonlinear implicit parameters used are:

 

A solver method is required to resolve Ax=b in each iteration of a nonlinear cycle. The linear implicit options used are:

 

The input nonlinear implicit options set in the FEM file are defined by NLPARMX:

 

NLPARM         9     100                                       P

+                   0.01

NLPARMX        9     0.0     0.1    0.01      -1      40

+           BFGS     ARC    1e-5    0.05    AUTO

+

+              6    1.02      20     0.8

Refer to the OptiStruct manual for more details about implicit options.

The nonlinear large deformation analysis has to be defined through a subcase. An NLPARM statement, as well as ANALYSIS=NLGEOM has to be present in the subcase. The termination time of 1.0s is defined through the TTERM entry.

SUBCASE       1

ANALYSIS NLGEOM

 SPC =       10

 NLPARM =        9

 NLOAD =        7

 TTERM = 1.000

Simulation Results and Conclusions

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Animations

The displacement, stresses (mises) and plastic strain results after the shearing of the joint are shown in the following figures.

Fig 5: Displacements (max = 2.84mm)

Fig 6: Stress (max = 1022 MPa)

Fig 7: Plastic strain in aluminum plates (max. = 23.86%).