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Finite-Element Sensitivity for Plasticity Using Complex Variable Methods
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DOI：10.1061/(ASCE)EM.1943-7889.0000837.png)
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The complex variable FEM (ZFEM) has been enhanced in this research to compute derivatives with respect to shape, material properties (elastic modulus, yield stress, plastic modulus, hardening parameters), and loads for a nonlinear solid mechanics model undergoing plastic deformation. This method presents a new and novel approach that uses complex variables to estimate derivatives within an incremental-iterative procedure for the solution of nonlinear finite-element equations. ZFEM offers significant advantages over real-valued finite-element analysis in that highly accurate derivative information may be obtained from a single analysis. The method has been implemented within a commercial finite-element software package using the user element and user material options. A strategy was developed to allow the software's solver algorithm to handle complex variable operations needed by ZFEM to perform sensitivity analysis. Numerical results confirm the high accuracy of the method through the analysis of a thick-walled cylinder case using perfectly plastic, bilinear hardening, and Ramberg-Osgood plasticity models. (C) 2014 American Society of Civil Engineers.
Keyword:
Complex step method
Nonlinear analysis
Sensitivity analysis
Plasticity
Perfectly plastic
Bilinear material
Ramberg-Osgood
Pressure vessel
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