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Finite Element Analysis (FEA) serves as the cornerstone of modern engineering design. However, its workflow is inherently complex and relies heavily on domain expertise. Although recent efforts have integrated Large Language Models (LLMs)…

人工智能 · 计算机科学 2026-05-29 Jiachen Zhang , Junyi Lao , Chenghao Liu , Siyuan Liu , Shixin Wu , Linsen Zhang , Boyu Wang , Songfang Huang

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

数值分析 · 数学 2016-03-30 Rebecca Conley , Tristan J. Delaney , Xiangmin Jiao

Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…

计算工程、金融与科学 · 计算机科学 2025-08-20 Tan Tran , Denisa Martonova , Sigrid Leyendecker

In this paper, we present a new immersed finite element scheme for solving elliptic interface problems on unfitted meshes by combining the skeletal finite element method (FEM) with the standard FEM. The skeletal FEM is used for the…

数值分析 · 数学 2025-09-17 Lin Yang , Qilong Zhai

Critically sized defects are currently treated via autologous or allograft bone grafting, distraction osteogenesis, and membrane induction. However, these methods have major weaknesses which encourage the development of synthetic bone graft…

组织与器官 · 定量生物学 2018-07-17 Rebecca Chung , Dilhan M. Kalyon , Antonio Valdevit

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…

计算工程、金融与科学 · 计算机科学 2021-12-08 Brandon Runnels , Vinamra Agrawal , Weiqun Zhang , Ann Almgren

This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…

数值分析 · 数学 2026-03-19 Hou Man , Chongmin Song , Sundararajan Natarajan , Ean Tat Ooi , Carolin Birk

Carbon fiber-reinforced composites (CFRC) are pivotal in advanced engineering applications due to their exceptional mechanical properties. A deep understanding of CFRC behavior under mechanical loading is essential for optimizing…

机器学习 · 计算机科学 2025-04-22 Zeping Chen , Marwa Yacouti , Maryam Shakiba , Jian-Xun Wang , Tengfei Luo , Vikas Varshney

This paper deals with the simulateneous optimization of a subset $\mathcal{O}_0$ of some domain $\Omega$ and its complement $\mathcal{O}_1 = \Omega \setminus \overline{\mathcal{O}}_0$ both considered as separate elastic objects subject to a…

数值分析 · 数学 2019-09-11 Patrick Dondl , Patrina S. P. Poh , Martin Rumpf , Stefan Simon

Additive manufacturing (AM) enables the development of high-performance architected cellular materials, emphasizing the growing importance of establishing programmable and predictable energy absorption capabilities. This study evaluates the…

应用物理 · 物理学 2024-02-27 Mattia Utzeri , Marco Sasso , Vikram S. Deshpande , S. Kumar

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

数值分析 · 数学 2024-03-20 Janina E. Schütte , Martin Eigel

Development of additive manufacturing in last decade greatly improves tissue engineering. During the manufacturing of porous scaffold, simplified but functionally equivalent models are getting focused for practically reasons. Scaffolds can…

图形学 · 计算机科学 2018-12-04 Ke Liu , Ye Guo , Zeyun Yu

This manuscript proposes an optimization framework to find the tailor-made functionally graded material (FGM) profiles for thermoelastic applications. This optimization framework consists of (1) a random profile generation scheme, (2) deep…

计算工程、金融与科学 · 计算机科学 2024-08-27 Piyush Agrawal , Ihina Mahajan , Shivam Choubey , Manish Agrawal

A framework based on FFT is proposed for micromechanical fatigue modeling of polycrystals as alternative to the Finite Element method (FEM). The variational FFT approach is used with a crystal plasticity model for the cyclic behavior of the…

计算物理 · 物理学 2019-05-23 Sergio Lucarini , Javier Segurado

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…

数值分析 · 数学 2023-10-24 Eric Parish , Payton Lindsay , Timothy Shelton , John Mersch

This work investigates the existing capabilities and limitations in numerical modeling of fracture problems in functionally graded materials (FGMs) by means of the well-known finite element code ABAQUS. Quasi-static crack initiation and…

材料科学 · 物理学 2017-11-02 Emilio Martínez-Pañeda , Rafael Gallego

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

计算工程、金融与科学 · 计算机科学 2025-06-24 Weihang Ouyang , Yeonjong Shin , Si-Wei Liu , Lu Lu

A novel modelling technique using finite element analysis to mimic the mechanoresponse of cell-laden biomaterial is proposed for the use in bioinks and other tissue engineering applications. Here a hydrogel-based composite biomaterial…

材料科学 · 物理学 2022-10-25 Abhinaba Banerjee , Sudipto Datta , Amit Roy Chowdhury , Pallab Datta

In this paper, the bending and the free flexural vibration behaviour of sandwich functionally graded material (FGM) plates are investigated using QUAD-8 shear flexible element developed based on higher order structural theory. This theory…

数值分析 · 数学 2012-04-11 S. Natarajan , M. Ganapathi

We present a novel image-based adaptive domain decomposition FEM framework to accelerate the solution of continuum damage mechanics problems. The key idea is to use image-processing techniques in order to identify the moving interface…

计算工程、金融与科学 · 计算机科学 2024-11-08 Panos Pantidis , Cornelius Otchere , Mostafa E. Mobasher