Slope constrained topology optimization

The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density{energy relation is assumed, including variable thickness sheet models and arti cial power laws. To ensure existence of solutions, the design set is restricted by enforcing pointwise bounds on the density slopes. A nite element discretization procedure is described, and a proof of convergence of nite element solutions to exact solutions is given, as well as numerical examples obtained by a continuation=SLP (sequential linear programming) method. The convergence proof implies that checkerboard patterns and other numerical anomalies will not be present, or at least, that they can be made arbitrarily weak