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This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…

Computational Engineering, Finance, and Science · Computer Science 2024-08-29 Hiroki Kobayashi , Katsuya Nomura , Yuqing Zhou , Masato Tanaka , Atsushi Kawamoto , Tsuyoshi Nomura

This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…

Numerical Analysis · Mathematics 2025-05-27 Jing-Ya Li , Hugo M. Verhelst , Henk den Besten , Matthias Möller

Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…

Machine Learning · Computer Science 2023-03-20 Giorgio Giannone , Faez Ahmed

A feature-mapping framework for inverse reconstruction of density-based topology optimization results is proposed. Unlike SIMP, whose voxelized outputs are hard to interpret or reuse, the method represents designs with high-level geometric…

Optimization and Control · Mathematics 2026-02-16 Patrick Jung

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…

Computational Engineering, Finance, and Science · Computer Science 2019-10-09 Nicolò Pollini , Oded Amir

Engineering design via CAD software relies on Non-Uniform Rational B-Splines (NURBS) as a means for representing and communicating geometry. Therefore, in general, a NURBS description of a given design can be considered the exact…

Numerical Analysis · Mathematics 2018-12-05 Norbert Hosters , Jan Helmig , Atanas Stavrev , Marek Behr , Stefanie Elgeti

This paper firstly presents an implementation of multi-material topology optimization (MTO) for in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates. The mathematical formulation of the MTO is…

Numerical Analysis · Mathematics 2023-09-29 Nam G. Luu , Thanh T. Banh

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with…

Numerical Analysis · Computer Science 2016-09-02 Gang Xu , Tsz-Ho Kwok , Charlie C. L. Wang

We propose a novel approach to the analysis of programmable geometrically exact shear deformable beam systems made of shape memory polymers. The proposed method combines the viscoelastic Generalized Maxwell model with the Williams, Landel…

Computational Engineering, Finance, and Science · Computer Science 2025-03-11 Giulio Ferri , Enzo Marino

This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid…

Computational Engineering, Finance, and Science · Computer Science 2024-12-25 Nikhil Singh , Prabhat Kumar , Anupam Saxena

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…

Computational Engineering, Finance, and Science · Computer Science 2021-08-09 Daniel Yago , Juan Cante , Oriol Lloberas-Valls , Javier Oliver

The paper presents a novel, parameter free, density evaluation method for topology optimization based on normalized product of a scalar field. The approach imposes length scale on solid phase implicitly and allows for pure 0-1 singularity…

Mathematical Physics · Physics 2022-08-25 Nikhil Singh , Anupam Saxena

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…

Numerical Analysis · Mathematics 2026-05-20 Jyotiranjan nayak , Shafeequdheen P , Vijayakrishna Rowthu

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…

Numerical Analysis · Mathematics 2017-07-11 Elena Atroshchenko , Gang Xu , Satyendra Tomar , Stephane P. A. Bordas

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides point-wise bound preserving design updates and faster convergence than other popular first-order topology optimization methods.…

Optimization and Control · Mathematics 2025-02-25 Brendan Keith , Dohyun Kim , Boyan S. Lazarov , Thomas M. Surowiec

Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential…

Numerical Analysis · Mathematics 2018-07-04 Giuseppe Pitton , Luca Heltai

Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…

This work presents a diffusion transformer framework for data-driven structural topology optimization that combines the accuracy of physics-based methods with the efficiency of generative deep learning. Conventional approaches such as the…

Computational Engineering, Finance, and Science · Computer Science 2026-05-05 Aaron Lutheran , Srijan Das , Alireza Tabarraei

Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D…

Numerical Analysis · Mathematics 2022-06-20 Xiao Xiao , Fehmi Cirak

The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…

Numerical Analysis · Mathematics 2017-02-17 Luca Heltai , Josef Kiendl , Antonio DeSimone , Alessandro Reali