doi:
UDK: 629.5.015.4

OPTIMIZED DESIGN OF BEAMS ON ELASTIC BASE

Миронов М. Ю.
Article language: русский

Annotation

The work is devoted to the control of stiffness and strength properties of structures placed on SEF - solid elastic foundations (distributed systems of compliant supports, soils, snow cover, calm liquid surface, fillers of three-layer composites). On the basis of matrix methods of sensitivity analysis, effective iterative algorithms for designing finite element models of beams on elastic foundations of constant and variable along the length of stiffness are constructed and programmatically implemented on the basis of satisfying the Kuhn-Tucker optimality conditions. Beam FEM is used in a variant of the displacement method, analytical and semi-analytical methods for obtaining derivatives from local, as well as integrally space-averaged constructions of displacements, the method of simple iterations with relaxation smoothing, methods for linearizing recurrent relations of optimality conditions and reducing the conditional minimization problem to an unconditional one using Lagrange multipliers . For a finite-element model of a non-prismatic beam on a control system with a large number of FE, the problems of configurations of the minimum mass under a distributed and localized load, with different ratios of the flexural rigidity of the structure and the rigidity of the base, are solved. It is proposed to use optimization as a computational substantiation of the system of intermediate reinforcements to increase the rigidity of the boundary layer between the shell and light filler in "sandwich" structures. Results suitable for application in the creation of effective three-layer structures from polymer composites are obtained. An effective control over the distribution of mass and stiffness over the structure with high relative gains in the isoperimetric formulation is shown. Directions for research into the influence of the nature of the distribution of the base stiffness and taking into account the transverse shear in the beam on the rational distributions of its bending stiffness along the length are determined. Keywords: indirect optimization methods, sensitivity analysis, beam finite elements, elastic foundation, localization effects, derivatives of displacements, Lagrange multipliers

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