АНАЛИЗ ЧУВСТВИТЕЛЬНОСТИ И ОПТИМИЗАЦИЯ ПОЛОГИХ СТЕРЖНЕВЫХ КОНСТРУКЦИЙ С УЧЕТОМ ГЕОМЕТРИЧЕСКОЙ НЕЛИНЕЙНОСТИ И ОГРАНИЧЕНИЙ НА УСТОЙЧИВОСТЬ

Abstract

The paper addresses the issue of sensitivity and the optimization of shallow rod structures with simultaneously varying the node coordinates, dimensions, cross-section areas, and with constraints on the critical total instability load, accounting for geometric nonlinearities, strength constraints. The material of the structures undergoing large displacements is assumed linearly elastic. All the external loads are considered conservative. Total loss of stability of a structure is interpreted as a singularity of its tangential stiffness matrix in critical points. The criteria for classifying the three types of the critical points - symmetric, asymmetric bifurcation points and a limit point - have been formulated. Special attention is paid to total loss of stability in limit points, characteristic of low or shallow rod structures, such as trusses, arches, cupolas, etc. To trace a fundamental curve of equilibrium states with limit points, the method of successive increments of displacements is used. Sensitivity of the critical load corresponding to a limit point has been analytically studied, and sensitivity of displacements of geometrically nonlinear structures has been analyzed. Sensitivity was analyzed using the direct method. A method for optimizing elastic shallow rod structures, accounting for geometric nonlinearities and stability constraints is presented. An additional condition in the considered optimization problem is the condition that limit points arise earlier than bifurcation ones. The methodology has been tested on benchmark structure - the spatial symmetric thirty-element aerial. The results obtained in the АNSYS medium, accounting for the linear and nonlinear analyses of stability are in good agreement with results published by foreign researchers for the behchmark structure.