Single-material structure topological optimization method and system considering structural stability

Abstract

The invention discloses a single-material structure topological optimization method and system considering structure stability, and belongs to the field of structure topological optimization. The method includes the following steps: constructing an optimization model which takes an expansion coefficient as a design variable, takes structure total flexibility minimization as a target and takes volume and buckling load factors as constraint conditions; calculating the total flexibility, volume and buckling load factor of the structure under the current expansion coefficient and the level set function; calculating a new expansion coefficient, and interpolating a new level set function; determining whether the difference between the current expansion coefficient and the reference value is smaller than a threshold value, if so, ending optimization, and determining the structure topology according to the current level set function; otherwise, continuing to optimize. Buckling load factor constraints based on expansion coefficients are introduced, the expansion coefficients are interpolated to obtain a level set function, the level set function determines pseudo-density, the pseudo-density determines a geometric stiffness matrix and a stiffness matrix, buckling load factors are solved through a characteristic equation, and the expansion coefficients influence the buckling load factors; therefore, the stability is considered, the optimization result is clearer, and the branches are more obvious.

Description

technical field [0001] The invention belongs to the field of structural topology optimization, and more specifically relates to a single-material structure topology optimization method and system considering structural stability. Background technique [0002] In the process of structural design, not only the strength and stiffness requirements of the structure must be considered, but also the stability of the structure under normal operating conditions must be ensured. In actual engineering, structures are usually composed of basic components such as beams, rods, and shells. If these members are under compression, their stability becomes an important factor affecting the safety of the structure. In fact, there have been many catastrophic accidents caused by the instability of basic components in history. Therefore, it is very necessary to consider the stability of the structure at the stage of structural conceptual design. Structural optimization technology can effectivel...

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Problems solved by technology

First of all, in actual engineering, the stiffness and stability of the structure are two important factors that designers must consider, but the existing topology optimization methods generally do not consider the stiffness and stability of the structure at the same time; secondly, most of the research done so far is based on SIMP (Solid Isotropic Microstructures with Penalization, Solid Isotropic Microstructure Model with Penalization Exponent) method, this method has the following disadvantages: the boundary of the optimized topological structure is not clear enough, especially when the filtering radius is relatively large

Disadvantages: Since the design variables are indirectly linked to the optimization problem, the approximation of some finite elements cut by the level set is involved in the middle, which affects the optimization accuracy

The continuous shape sensitivity of linear elastic bodies has been well developed, but the continuous shape sensitivity of nonlinear structures is very difficult to obtain and requires a high mathematical foundation

Many structural topology optimization methods based on parametric level set methods in the prior art do not consider structural stability

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