A New Homogenization Formulation for Multifunctional Composites

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.

Numerical treatment of acoustic problems with the smoothed finite element method

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.

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.

To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell‐based smoothed FEM (ICS‐FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS‐FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS‐FEM provides a continuous system with a close‐to‐exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS‐FEM, we investigated several numerical examples and found that ICS‐FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

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

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

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

A smoothed finite element method using second-order cone programming

An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems

A new smoothed finite element method (S-FEM) is proposed using hybrid smoothing operations based on nodes and edges of the mesh for static and free vibration analyses of plates governed by the Reissner---Mindlin plate theory. In the present approach, both the node-based smoothed finite element method (NS-FEM) and edge-based smoothed finite element method (ES-FEM) are utilized in a careful designed manner to overcome the shear locking. The formulations use 3-node triangular elements for easy automatic mesh creation, and linear interpolation functions are used for simplicity and robustness. The bending strains field are smoothed by the means of gradient smoothing technique over smoothing domains constructed by element edges, while the shear strains filed is smoothed based on the combination of NS-FEM and ES-FEM with a proper weightage controlled by a coefficient. A simple formula is developed for automatic selection of the coefficient by considering mesh size and thickness of the plate. For easy reference, the present technique is termed as NS+ES-FEM. The numerical examples demonstrate that the proposed method passes the shear-locking test and improves accuracy of the solution.

Thermoelastic analysis by means of three-dimensional polyhedral elements based on the Smoothed Finite elements method (S-FEM), for example nodal Cell-based S-FEM (CS-FEM), Node-based S-FEM (NS-FEM), and Edge-based S-FEM (ES-FEM), was studied. S-FEM allows implicit shape functions, making it possible to construct shape functions of S-FEM based polyhedral elements in a straightforward manner. The performance of S-FEM based polyhedral elements was compared with one another and with the conventional finite elements including hexahedral and tetrahedral element. Numerical examples show that the polyhedral elements by means of CS-FEM and ES-FEM provide better accuracy and convergence rate than conventional hexahedral finite elements, while the polyhedral elements by means of NS-FEM leads to spurious mode.

． 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 a technique to evaluate the fracture parameters by combining the edge based smoothed finite element method (ESFEM) and the scaled boundary finite element method (SBFEM). A semi-analytical solution is sought in the region close to the vicinity of the crack tip using the SBFEM, whilst, the ESFEM is used for the rest of the domain. As both methods satisfy the partition of unity and the compatibility condition, the stiffness matrices obtained from both methods can be assembled as in the conventional finite element method. The stress intensity factors (SIFs) are computed directly from their definition. Numerical examples of linear elastic bodies with cracks are solved without requiring additional post-processing techniques. The SIFs computed using the proposed technique are in a good agreement with the reference solutions. A crack propagation study is also carried out with minimal local remeshing to show the robustness of the proposed technique. The maximum circumferential stress criterion is used to predict the direction of propagation.

Improved element-particle coupling strategy with δ-SPH and particle shifting for modeling sloshing with rigid or deformable structures