Polyhedral smoothed finite element method for thermoelastic analysis

A new concept of smoothed finite element method (S-FEM) using 10-node tetrahedral (T10) elements, CS-FEM-T10, is proposed. CS-FEM-T10 is a kind of cell-based S-FEM (CS-FEM) and thus it smooths the strain only within each T10 element. Unlike the other types of S-FEMs [node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM), and face-based S-FEM (FS-FEM)], CS-FEM can be implemented in general finite element (FE) codes as a piece of the element library. Therefore, CS-FEM-T10 is also compatible with general FE codes as a T10 element. A concrete example of CS-FEM-T10 named SelectiveCS-FEM-T10 is introduced for large deformation problems of nearly incompressible solids. SelectiveCS-FEM-T10 subdivides each T10 element into 12 four-node tetrahedral (T4) subelements with an additional dummy node at the element center. Two types of strain smoothing are conducted for the deviatoric and hydrostatic stress evaluations and the selective reduced integration (SRI) technique is utilized for the stress integration. As a result, SelectiveCS-FEM-T10 avoids the shear/volumetric locking, pressure checkerboarding, and reaction force oscillation in nearly incompressible solids. In addition, SelectiveCS-FEM-T10 has a relatively long-lasting property in large deformation problems. A few examples of large deformation analyses of a hyperelastic material confirm the good accuracy and robustness of SelectiveCS-FEM-T10. Moreover, an implementation of SelectiveCS-FEM-T10 in the FE code ABAQUS as a user-defined element (UEL) is conducted and its capability is discussed.

본 연구에서는 다면체 요소의 개발을 위하여 Wachspress 좌표계와 이동최소자승 근사를 기반으로하는 형상함수와 수치적분 방법을 제시하고 있다. 사면체 요소를 사면체 영역으로 분할하여 형상함수가 구성이 되고 이 영역을 사용한 일관성있는 수치적분이 수행되게 된다. 다면체 요소 면에서 Wachspress 좌표계를 사용하고 요소 내부에서 라플라스 방정식을 적용하여 이동최소자승 근사의 가중함수를 정의하게 된다. 본 연구에서 개발되는 다면체 요소의 형상함수와 수치적분 방법은 일반적인 유한요소와 유사한 특성을 갖게 되는데 수치 예제를 통하여 유효성을 보여주었다. In this paper, a polyhedral element is presented to solve three-dimensional problems by developing shape functions based on Wachspress coordinates and moving least square approximation. A subdivision of polyhedrons into tetrahedral domains is performed for the construction of shape functions of polyhedral elements, and numerical integration of the weak form is carried out consistently over the tetrahedral domains. The weight functions for moving least square approximation are defined by solving Laplace equation with boundary values based on Wachspress coordinates on polyhedral element faces. Polyhedral elements presented in this paper have similar properties to conventional finite element regarding the continuity, the completeness, the node-element connectivity and the inter-element compatibility. Numerical examples show the effectiveness of the present method for solving three-dimensional problems using polyhedral elements.

Periodic microstructural composites have gained considerable attention in material science and engineering attributable to their excellent flexibility in tailoring various desirable physical properties. Conventionally, the finite element technique has been widely used in implementing the homogenization. However, the standard finite element method (FEM) leads to an overly stiff model which sometimes gives unsatisfactory accuracy especially using triangular elements in 2D or tetrahedral elements in 3D with coarse mesh. In this paper, different forms of smoothed finite element method (SFEM) are presented to develop new asymptotic homogenization techniques for analyzing various effective physical properties of periodic microstructural composite materials. A range of multifunctional material examples, including elastic modulus with multiphase composites, conductivity of thermal and electrical composites, and diffusivity/permeability of 3D tissue scaffold, has exemplified herein to demonstrate that SFEM is able to provide more accurate results using the same set of mesh compared with the standard FEM. In addition, the computational efficiency of SFEM is also higher than that of the standard FEM counterpart.

The development of integrated circuit (IC) packaging is one of the important factors for the advanced production of the semi-conductor industry. With the recent rise of innovative demand of the production technology, lot of issues had been raised at the manufacturing level especially at back-end production. In order to solve the problem, finite element analysis (FEA) is one of the methods that has been broadly used to evaluate the internal stress of IC package. The performance effect of tetrahedral or hexahedral dominance elements in the meshing stage may lead to the unswerving of FEA results. In such condition, the performance of the element type needs to be analyzed in order to determine which implementation leads to result with higher confident level. This study used the quasi-static simulation of FEA to determine the performance of tetrahedral and hexahedral dominance elements in FEA of IC package strength. The monitored stress was focused on the component levels of IC package, the die and the diepad. The IC package is modelled in three-dimensional case which represented as close as the actual product by simplifying certain parts. The performance evaluation had considered the effect of grid independent study for each of the element type. The maximum stress produced by using the tetrahedral element had been compared with the stress produced by the hexahedral dominance elements. Comparison of the performance showed that the value of the maximum stress produced from hexahedral dominance element was significantly higher at 16% to 40% than the solution obtained from the tetrahedral element. It is found that by using hexahedral element in the finite element analysis, a significant higher value of Von Mises stress is produced, which is more than 505 MPa in diepad. This stress value has been established by previous study within the plastic deformation range and also has good agreement with the physical examination.Â

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects; 2) upper-bound solutions; 3) accurate solutions and higher convergence rates; 4) insensitivity to mesh distortion; 5) Jacobian-free; 6) volumetric-locking-free; and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

An accurate coupled method for analysis of transcranial magneto-acoustic-electrical stimulation

Numerical treatment of acoustic problems with the smoothed finite element method

Periodic mesh generation and homogenization of inclusion-reinforced composites using an element-carving technique with local mesh refinement

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid–structure interactions (FSIs) and the high–frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R2 = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p < 0.001), while the pressure response was dependent on the shock tube mesh size (p < 0.001). The results of this study highlight the necessity for mesh sensitivity analysis in blast models.

A coupled smoothed finite element method (S-FEM) for structural-acoustic analysis of shells

This paper describes the development of a software to perform three-dimensional crack propagation analyses. The software is based on the conventional finite element method with second order tetrahedral element and an automatic mesh generation software. Hexahedral finite elements have historically been used in fracture analyses and methodologies to compute the crack parameters have been developed for the hexahedral elements. In present research, the authors have developed a VCCM (virtual crack closure-integral method) for the second order tetrahedral finite element. Use of the tetrahedral element allows us to utilize an automatic mesh generation software. The direction and rate of crack propagation are predicted based on the stress intensity factors and the shape of crack is updated. Hence, a software package containing the modules for mesh generation, for finite element analysis, for stress intensity factor evaluation, for predicting the rate and the direction of crack propagation and for updating crack configuration, can be developed.

． Kay Words：Bubble -enhanced edge -based smoodled 且nite element method ( bES -FEM ) ， Large defbnnaUon ， Nearly incompressible ， Volumetric Locking， Pressure oscillation ， Bubble 血 nction

This paper presents two-dimensional boundary value problems of the stress-based gradient elasticity within the smoothed finite element method (S-FEM) framework.Gradient elasticity is introduced to address the limitations of classical elasticity, particularly its struggle to capture size-dependent mechanical behavior at the micro/nano scale.The Ru-Aifantis theorem is employed to overcome the challenges of high-order differential equations in gradient elasticity.This theorem effectively splits the original equation into two solvable second-order differential equations, enabling its incorporation into the S-FEM framework.The present method utilizes a staggered scheme to solve the boundary value problems.This approach efficiently separates the calculation of the local displacement field (obtained over each smoothing domain) from the non-local stress field (computed element-wise).A series of numerical tests are conducted to investigate the influence of the internal length scale, a key parameter in gradient elasticity.The results demonstrate the effectiveness of the proposed approach in smoothing stress concentrations typically observed at crack tips and dislocation lines.

Automatic mesh generation for 3D smoothed finite element method (S-FEM) based on the weaken-weak formulation