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Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…

Numerical Analysis · Mathematics 2025-02-21 Eloi Martinet , Leon Bungert

In this paper we use memory-distributed level set-based topology optimisation to design three-dimensional periodic piezoelectric materials with enhanced properties. We compare and assess several existing iterative solvers with respect to…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Zachary J. Wegert , Anthony P. Roberts , Vivien J. Challis

An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…

Numerical Analysis · Mathematics 2017-11-15 Cristian Barbarosie , Sérgio Lopes , Anca-Maria Toader

We propose a novel level set-based topology optimization for micropolar solids subjected to thermo-mechanical loading. To capture the size effects, we have incorporated the microstructural length-scale information into the level set-based…

Computational Physics · Physics 2026-01-21 Mayank Shekhar , Ayyappan Unnikrishna Pillai , Subhayan De , Mohammad Masiur Rahaman

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…

Optimization and Control · Mathematics 2025-03-28 Luis Irastorza-Valera , Ricardo Larraínzar-Garijo , Javier Montoya-Adárraga , Luis Saucedo-Mora

Topology optimization is widely used by engineers during the initial product development process to get a first possible geometry design. The state-of-the-art is the iterative calculation, which requires both time and computational power.…

Machine Learning · Computer Science 2021-09-30 Alex Halle , L. Flavio Campanile , Alexander Hasse

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…

Optimization and Control · Mathematics 2023-03-22 Tomoyuki Oka , Takayuki Yamada

We propose a neural network-based computational framework for the simultaneous optimization of structural topology, curved layers, and path orientations to achieve strong anisotropic strength in fiber-reinforced thermoplastic composites…

Machine Learning · Computer Science 2025-05-08 Tao Liu , Tianyu Zhang , Yongxue Chen , Weiming Wang , Yu Jiang , Yuming Huang , Charlie C. L. Wang

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

Optimization and Control · Mathematics 2023-04-25 Ruichen Jiang , Nazanin Abolfazli , Aryan Mokhtari , Erfan Yazdandoost Hamedani

Topology optimization produces designs with intricate geometries and complex topologies that require advanced manufacturing techniques such as additive manufacturing (AM). However, insufficient consideration of manufacturability during the…

Computational Engineering, Finance, and Science · Computer Science 2025-02-28 Seungheon Shin , Byeonghyeon Goh , Youngtaek Oh , Hayoung Chung

We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…

Optimization and Control · Mathematics 2013-07-30 Michal Kocvara

A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…

Numerical Analysis · Computer Science 2016-04-04 Samir Omerović , Thomas-Peter Fries

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…

Optimization and Control · Mathematics 2016-12-14 Igor Ostanin , Ivan Tsybulin , Mikhail Litsarev , Ivan Oseledets , Denis Zorin

Functionally Graded Materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Shiguang Deng , Horacio D. Espinosa , Wei Chen

This paper demonstrates the computational design of soft elastomeric pneumatic actuators using nonlinear topology optimization. An existing density- and porohyperelasticity-based topology optimization framework was extended from 2D to 3D…

Robotics · Computer Science 2026-05-20 Sumit Mehta , Konstantinos Poulios

The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…

Computational Engineering, Finance, and Science · Computer Science 2020-06-09 Xiaodong Huang

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both…

Numerical Analysis · Mathematics 2022-06-29 G. A. Haveroth , C-J. Thore , M. R. Correa , R. F. Ausas , S. Jakobsson , J. A. Cuminato , A. Klarbring

We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid…

Computational Engineering, Finance, and Science · Computer Science 2021-05-21 Li Zheng , Siddhant Kumar , Dennis M. Kochmann

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…

Numerical Analysis · Mathematics 2026-05-15 Peter Gangl , Brendan Keith , Dohyun Kim , Boyan S. Lazarov , Thomas M. Surowiec

This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…

Optimization and Control · Mathematics 2026-03-25 Jan Oellerich , Takayuki Yamada
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