Abstract. The improved mathematical model of steel frame structures' design is created. The loading is simple, and plastic strains are evaluated. Energy principles of deformable body mechanics and mathematical programming theory are employed. Equilibrium finite elements with interpolation functions of internal forces are used for discretization. The elements are designed using HE, IPE, RHS steel profile assortments and considering dispersion of geometrical characteristics of profile assortment sets. Optimal design of steel structures is realized by using the experimental tool system JWM SAOSYS Toolbox v0.42, which was created by the authors in MATLAB environment. SAOSYS architecture operates with objectoriented finite elements pseudo-polymorphously. The possibilities of this system are demonstrated by considering a numerical example of optimal design of industrial building frame with strength and stiffness constraints. The assumption of small displacements is adopted for computations.

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A circular reinforced concrete plate on deformable foundation is investigated. The foundation is composed of three layers of soil which are defined as isotropically nonlinear materials with variable physical properties. The reinforced plate is treated as an elastic body. The plate is subjected to dissymmetrical half-circular loading of linearly variable pressure. Generally, the unified system "structure-foundation" is the contact analysis problem, which is modeled by ANSYS software. Plastic shear deformations are evaluated by solving the contact problem by the finite element method. The comparative analysis, including the treatment of physically linear system "structure-foundation", is performed. The comparison based on linear analysis shows that rigidity of the foundation generates higher extreme stresses in the plate in terms of the Huber-Mises criterion. However, in nonlinear analysis, the intensity of stresses is naturally decreasing, when a more flexible model of the foundation is used.

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