SUMMARYThe direct boundary element method based on the Rayleigh-Green identity is employed for the static analysis of Kirchhoff plates. The starting point is a slightly modified version of Stern's equations. The focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w. The concept of element matrices is developed and the Cauchy principal values of the singular integrals are given in detail. The treatment of domain integrals, the handling of internal supports, the properties of the solution and the effect of singularities are discused. Numerical examples ilIustrate the various techniques. In the appendix the influence functions for the second and third derivatives of the deflection w are given.

For FE-based structural optimiza.tion systems, a. large variety of different numerical algorithms ia ava.i\able, e.g. sequential linear programming, sequential quadratic programming, convex approximation, generalized reduced gradient, multiplier, penalty or optimality criteria. methods, and combina.tions of these approaches. The purpose of the pa.per is to present the numerical reaults of a comparative study of eleven rnathematical programrning codes which represent typical realizations of the mathema.tical methods mentioned. They a.re implemented in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis. The comparative results are obtained from a collection of79 test problems. The majority ofthem are academic test cases, the others possess some practical reßlliJe background. Optirnization is performed with respect to sizing of trusses and bearns, wall thicknesses, etc., subject to stress, displacement, and many other constraints. Numerical cornparison is based on reliability and efficiency measured by calculation time ana number of analyses needed to reach a certain accura.cy level.

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