DESIGN SENSITIVITY ANALYSIS IN DYNAMIC THERMOVISCOELASTICITY WITH IMPLICIT INTEGRATION

Design sensitivity equations for coupled thermoviscoelastic systems ar e discretized via the finite element method. The approach is developed for structural systems by using the total Lagrangian approach and the reference domain concept. The discretization is based on implicit int egration schemes. The implementation of finite element and design sens itivity analysis utilizes the Christensen-Naghdi free energy function and the direct differentiation approach, which is most suitable for th e systems under consideration. A relationship between the discretized sensitivity equations and the equations for the original analysis is s hown. Use of the same discretization for analysis and sensitivity anal ysis is emphasized. Partial derivatives of the right-hand side require d for sensitivity calculations are implemented via the central differe nce method, which provides greater flexibility without sacrificing acc uracy. Examples of analysis and design sensitivity analysis for a ther moviscoelastic non-linear truss and a plate with a hole are given. The calculated sensitivity results are verified by comparison with overal l finite difference calculations.