A Linear Programming-Based Method for Estimating the Static Displacement Boundary of Structures Containing Convex Polyhedral Uncertainty Parameters

Abstract

The invention discloses a method for evaluating the static force displacement boundary of a structure containing convex polyhedron uncertainty parameters based on linear programming. This method considers the uncertain parameters of the convex polyhedron. First, the convex polyhedron model of the static response problem of the uncertain structure is established. Through vector and matrix transformation and operation, the convex polyhedron model of the static response problem of the uncertain structure is completed to the The transformation of the standard form of the linear programming problem; furthermore, a series of linear programming sub-problems are formed by combining the vertex matrices of the structural stiffness convex polyhedron and the vertex vectors of the external load convex polyhedron; finally, based on the linear programming theory, a To solve a series of linear programming sub-problems feasible domain vertex values, use the vector transformation formula to express the maximum value and minimum value of a series of vertex values ​​as the upper bound and lower bound of the static displacement boundary, thus realizing the precise static displacement boundary Evaluate.

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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