Method for evaluating a static displacement boundary of a structure with convex polyhedron uncertainty parameters based on linear programming

Abstract

A method for evaluating a static displacement boundary of a structure with convex polyhedron uncertainty parameters based on linear programming is disclosed. The method comprises that: considering theuncertainty parameters of the convex polyhedron, the convex polyhedron model of the static response of the uncertainty structure is established. The standard form of the linear programming problem istransformed from the convex polyhedron model of the static response of the uncertainty structure by vector and matrix transformation and operation. Furthermore, a series of linear programming subproblems are formed by combining the vertex matrices of stiffness convex polyhedron and the vertex vectors of external load convex polyhedron. Finally, based on the linear programming theory, the vertex values of feasible region of a series of linear programming subproblems are solved, and the maximum and minimum values of a series of vertex values are expressed as the upper and lower bounds of staticdisplacement boundary respectively by using vector transformation formula, thus the accurate evaluation of static displacement boundary is realized.

Description

technical field [0001] The invention belongs to the technical field of uncertainty propagation analysis under the condition of convex polyhedron uncertainty parameters, and particularly relates to a method based on linear programming to evaluate the static force displacement boundary of structures containing convex polyhedron uncertainty parameters, which is realized under the guidance of linear programming theoretical methods The accurate evaluation of the precise boundary of the static displacement of structures with convex polyhedral uncertain parameters provides a theoretical basis for the accurate characterization of the mechanical behavior boundaries of structures with uncertain parameters. Background technique [0002] In structural design and analysis, uncertainties in material properties, structural dimensions and loading conditions widely exist. Traditional structural static problems are analyzed and solved based on deterministic models. With the development of sc...

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Problems solved by technology

However, interval models represent uncertain variables with independent intervals, ignoring the correlation between uncertain variables, and often get too wide boundaries

At present, for the evaluation of the static displacement of structures with relevant uncertain parameters, the interval model fails to obtain accurate displacement boundaries, which often loses practical application significance due to the phenomenon of "overestimation", and cannot provide objective information for structural reliability evaluation and design. valid data

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