相关论文: Numerical analysis of the SIMP model for the topol…

The need for optimized structures with good mechanical performance for the minimum weight is common in industry. Solid Isotropic Material with Penalization (SIMP) is a Topology Optimization (TO) method offering a trade-off between minimum…

This study investigates the impact of finite element selection on structural topology optimization using the SIMP (Solid Isotropic Material with Penalization) method. Specifically, it compares linear (P1) and quadratic (P2) triangular…

The focus of this paper is on topology optimization of continuum structures subject to thermally induced buckling. Popular strategies for solving such problems include Solid Isotropic Material with Penalization (SIMP) and Rational…

The area of topology optimization of continuum structures of which is allowed to change in order to improve the performance is now dominated by methods that employ the material distribution concept. The typical methods of the topology…

Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…

Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…

Shell structures with a high stiffness-to-weight ratio are desirable in various engineering applications. In such scenarios, topology optimization serves as a popular and effective tool for shell structures design. Among the topology…

The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional…

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

This paper addresses the properties of Continuous Interior Penalty (CIP) finite element solutions for the Helmholtz equation. The $h$-version of the CIP finite element method with piecewise linear approximation is applied to a…

T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel…

In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as ``the simple method'') optimizes a design using only…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

This paper presents a topology optimization framework for structural problems subjected to transient loading. The mechanical model assumes a linear elastic isotropic material, infinitesimal strains, and a dynamic response. The optimization…

We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…

We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…