A common algorithm for various parametric geometric changes in finite element design sensitivity computation

Design sensitivity analysis is mainly applicable to optimization and force computation problems. With the former, geometrical parameters undergo big changes that require mesh integrity checks and mesh connections need to be preserved for C1 continuity. This is usually addressed through problem-specific mesh generators that cannot be general purpose. This paper presents a new criterion for changing meshes for design sensitivity computation while preserving C1 continuity of the object function. It is shown to be applicable to various kinds of linear changes of multiple parameters that combine to model changes of nodes, lines and objects. This is used to create a powerful general-purpose parameterized mesh generator for linear and rotary displacement in finite element sensitivity computation. The powerful algorithm developed here for linear movement is shown through example to work for several types of parameters. This generator allows repeated solutions with iterated meshes so that it can be employed in a first-order optimization strategy exploiting its faster convergence.