Topological optimization method for progressive structure containing maximum size constraints

Abstract

The invention belongs to the related technical field of structure optimization and discloses a topological optimization method for a progressive structure containing maximum size constraints , which comprises the following steps of: (1) performing finite element discretization on a design domain of a structure to be optimized, calculating to obtain a structure flexibility value and a local size measure, further adopting P norm condensation to obtain a global measure, and updating a Lagrange multiplier lambda to obtain an adjoint solution; (2) calculating a sensitivity value of each discrete unit; (3) sorting the sensitivity values of the discrete units according to the sizes, and then adding, deleting and updating the material of the to-be-optimized structure; (4) calculating the variationdelta c of the sum of the compliance corresponding to each iteration of five steps, comparing the obtained variation delta c with 1%, and if delta c is less than or equal to 1% and the allowable material consumption fraction of the structure to be optimized reaches a set value, ending, thereby completing the optimization of the structure to be optimized; otherwise, turning to the step (1). According to the invention, the efficiency and stability are improved.

Description

technical field [0001] The invention belongs to the technical field related to structure optimization, and more specifically relates to a progressive structure topology optimization method with maximum size constraints. Background technique [0002] Structural topology optimization design method is a new digital structure design method. By establishing a mathematical model including objective functions and constraint equations, finite element numerical analysis is carried out on the structure, and in the design domain, iteratively obtains structures that meet the target requirements according to optimization criteria or mathematical programming methods. Material distribution, structural topology optimization design methods are widely used in body design, aerospace, communication electronics and other structural design. [0003] At present, some studies have been done by those skilled in the art, such as document 1 "James K. Guest (2009) Imposing maximum length scale in topol...

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Problems solved by technology

However, the topology optimization method adopted in Document 1 is based on the density variable method, the design variable can continuously take values ​​between 0 and 1, and there are gray-scale units in the structure, so it is difficult to accurately evaluate the current size of the structure; and most of the other proposed methods are computationally efficient Low, size constraints are difficult to be strictly satisfied

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