An asymptotically concentrated method for structural topology optimization based on the SIMLF interpolation

Abstract

Summary In this work, an asymptotically concentrated topology optimization method based on the solid isotropic material with logistic function interpolation is proposed. The asymptotically concentrated method is introduced into the process of optimization cycle after updating the design variables. At the same time, with the use of the solid isotropic material with logistic function interpolation, all the candidate densities are reasonably polarized, relying on the characteristic of the interpolation curve itself. The asymptotically concentrated method can effectively suppress the generation of intermediate density and speed up the process of updating the design variables, hence improving the optimization efficiency. Moreover, the above polarization can weaken the influence of low‐related‐density elements and enhance the influence of high‐related‐density elements. For the single‐material topology optimization problem, gray‐scale elements can be effectively eliminated, and clear boundary and smaller compliance can be obtained by this method. For the multimaterial topology optimization problem, minimum compliance with high efficiency can be achieved by this method. The proposed method mainly includes the following advantages: concentrated density variables, reasonable interpolation, high computational efficiency, and good topological results.

Nodal Cosine Sine Material Interpolation in Multi Objective Topology Optimization With the Global Criteria Method for Linear Elasto Static, Heat Transfer, Potential Flow and Binary Cross Entropy Sharpening

“…If these interpolation function should be related to composite structures the Hashin-Shtrikman bounds should be stasified (Hashin and Shtrikman, 1963). In our approach we need to violate that criterion similar to (Cui et al, 2018;Du et al, 2015) to provide a interpolation strategy ensuring smooth material distribution in the element. We compare that logistic function and the SIMP method with a trigonometric interpolation strategy.…”

“…The most common element material interpolation function is the solid isotropic material with penalization (SIMP) based on design variables for elements (Bendsøe and Sigmund, 1999). That approach was extended in changing the interpolation function (Cui et al, 2018;Du et al, 2015) or using a node-based material interpolation field (Guest, 2009;Guest et al, 2004;Kang and Wang, 2012;Rahmatalla and Swan, 2004). So, in contrast to SIMP, the authors of (Cui et al, 2018;Du et al, 2015) chooses a logistic material interpolation function with different parameters applied to the elements.…”

An Improved Guide-Weight Method Without the Sensitivity Analysis

“…where q is the weight coefficient of the RAMP interpolation model. Substituting equation (28) into equations (16) and (21) yields…”

“…There are many modelling methods to be presented, including homogenization method [3], [4], variable density method [5], [6], level set method [7], [8], evolutionary structural optimization method [9], [10], phase field method [11], [12], independent continuous mapping method [13], [14] and topological derivative method [15]. Cui et al [16] introduced the asymptotically concentrated method into multi-material topology optimization and proposed a new topology optimization method based on the solid isotropic material with logistic function interpolation. The method can not only effectively suppress the generation of intermediate density, but also improve the optimization efficiency.…”

Periodic Topology Optimization of a Stacker Crane

“…Periodic feature structures have attracted the attention of academic and industrial technicians with their unique structural form, excellent visual aesthetics, extensibility in array direction, physical versatility, and good manufacturing and design [20]- [25]. Many topology optimization methods have been presented to research periodic topology optimization, including the homogenization method, evolutionary structural optimization method [26]- [29], and independent continuous mapping method [30], [31].…”