A Progressive Structural Topology Optimization Method with Maximum Size Constraints

Abstract

The invention belongs to the technical field related to structural optimization, and discloses a progressive structural topology optimization method containing maximum size constraints, the steps of which are: (1) performing finite element discretization on the design domain of the structure to be optimized, and calculating the structural compliance value and local size measure, and then use the P norm to condense to obtain the global measure, and update the Lagrangian multiplier λ to obtain the adjoint solution; (2) calculate the sensitivity value of each discrete unit; (3) convert the discrete unit The sensitivity values ​​are sorted according to the size, and then the materials of the structure to be optimized are added, deleted and updated; (4) Calculate the amount of change Δ of the sum of compliance corresponding to five steps of each iteration c , will get the variation Δ c Compared with 1%, if Δ c If it is less than or equal to 1% and the allowable material usage fraction of the structure to be optimized reaches the set value, then end, thereby completing the optimization of the structure to be optimized; otherwise, go to step (1). The invention improves efficiency and stability.

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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