NONLINEAR STRUCTURAL DESIGN SENSITIVITY ANALYSIS FOR PATH DEPENDENT PROBLEMS .2. ANALYTICAL EXAMPLES

In Part 1 of this paper a general theory of design sensitivity analysis for nonlinear structures with history dependent effects is given. The theory is also reduced to several special cases to show its generality. In the present paper, three examples are used to analytically verify the theory. Both the adjoint structure method (ASM) and the direct differentiation method (DDM) are demonstrated. The examples are (1) reaction force sensitivity for an indeterminate beam, (2) displacement sensitivity for several cases of an axial force element and (3) stress and displacement sensitivities for a visco-elastic problem. These examples provide insights for numerical implementation of the theory for more complex design problems. © 1990.