SHAPE DESIGN SENSITIVITY ANALYSIS OF VISCOPLASTIC STRUCTURES

Design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from Hamilton's principle. Constitutive models based on internal variable theory are incorporated in response analysis. Such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface. The direct variation method is employed to obtain the sensitivity of the response. Discretization of the analysis and sensitivity equations, and computer implementation aspects are discussed. The discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory. In the numerical examples, only material nonlinearity under quasi-static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations. The accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method. Cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation.