A BOUNDARY CONTOUR FORMULATION FOR DESIGN SENSITIVITY ANALYSIS IN 2-DIMENSIONAL LINEAR ELASTICITY

A formulation for computing first-order shape design sensitivities in two-dimensional (2-D) linear elastostatics by the boundary contour met hod (BCM), along with a numerical implementation using quadratic bound ary elements, is presented in this paper. Here, the direct differentia tion approach is analytically applied to the appropriate boundary cont our equations in order to derive the sensitivities of all the physical quantities (displacements, tractions and stresses) on the boundary as well as those for displacements and stresses inside the body under co nsideration. The nonsingular formulation of the BCM is used for comput ing the boundary displacements, and boundary stresses at ''off contour '' regular points. A regular boundary point is a point on the boundary where it is locally smooth; an off contour point lies inside a bounda ry element. Their corresponding sensitivities are obtained in a straig htforward manner from the resulting regular sensitivity formulation. A lso, the stress sensitivities at the boundary nodes can be recovered e asily from the global displacement shape functions described in a Cart esian coordinate system. Finally, through three numerical examples for which analytical solutions exist, it is shown that the BCM can provid e remarkably accurate numerical results for shape sensitivities. (C) 1 998 Elsevier Science Ltd.