Design sensitivity analysis in dynamic thermoviscoelasticity with implicit integratio

Design sensitivity equations for coupled thermoviscoelastic systems are 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 integration schemes. The implementation of finite element and design sensitivity analysis utilizes the Christensen-Naghdi free energy function and the direct differentiation approach, which is most suitable for the systems under consideration. A relationship between the discretized sensitivity equations and .the equations for the original analysis is shown. Use of the same discretization for analysis and sensitivity analysis is emphasized. Partial derivatives of the right-hand side required for sensitivity calculations are implemented via the central difference method, which provides greater flexibility without sacrificing accuracy. Examples of analysis and design sensitivity analysis for a thermoviscoelastic non-linear truss and a plate with a hole are given. The calculated sensitivity results are verified by comparison with overall finite difference calculations