Z.C. He

AN IMPROVED MODAL ANALYSIS FOR THREE-DIMENSIONAL PROBLEMS USING FACE-BASED SMOOTHED FINITE ELEMENT METHOD

In this work, we further extended the face-based smoothed finite element method (FS-FEM) for modal analysis of three-dimensional solids using four-node tetrahedron elements. The FS-FEM is formulated based on the smoothed Galerkin weak form which employs smoothed strains obtained using the gradient smoothing operation on face-based smoothing domains. This strain smoothing operation can provide softening effect to the system stiffness and make the FS-FEM provide more accurate eigenfrequency prediction than the FEM does. Numerical studies have verified this attractive property of FS-FEM as well as its ability and effectiveness on providing reliable eigenfrequency and eigenmode prediction in practical engineering application.

Acoustic analysis using a mass-redistributed smoothed finite element method with quadrilateral mesh

Purpose – In this work, an SFEM is proposed for solving acoustic problems by redistributing the entries in the mass matrix to “tune” the balance between “stiffness” and “mass” of discrete equation systems, aiming to minimize the dispersion error. The paper aims to discuss this issue. Design/methodology/approach – This is done by simply shifting the four integration points’ locations when computing the entries of the mass matrix in the scheme of SFEM, while ensuring the mass conservation. The proposed method is devised for bilinear quadratic elements. Findings – The balance between “stiffness” and “mass” of discrete equation systems is critically important in simulating wave propagation problems such as acoustics. A formula is also derived for possibly the best mass redistribution in terms of minimizing dispersion error reduction. Both theoretical and numerical examples demonstrate that the present method possesses distinct advantages compared with the conventional SFEM using the same quadrilateral mesh. O...

Topology Optimization Using Node-Based Smoothed Finite Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

Stability analysis of generalized mass formulation in dynamic heat transfer

ABSTRACT In this article, the generalized mass formulation is developed in an explicit analysis of transient transport problems. It has been well known that the time step is typically smaller in explicit analysis than in implicit analysis when the same size mesh is used. Further, the over-stiffness of conventional finite-element model may result in poor accuracy with linear triangular or tetrahedral elements. In order to improve the computational efficiency and numerical accuracy, this article proposes a generalized mass formulation by matching the mass matrix to the smoothed stiffness matrix using linear triangular elements in 2-D problems. The proposed mass matrix can be obtained by simply shifting the integration points from the conventional locations. Without loss of generality, several 2-D examples, including conduction, convection, and radiation heat transfer problems, are presented to demonstrate that the generalized mass formulation allows a larger time step in explicit analysis compared with the lumped and consistent mass matrices. In addition, it is found that the maximum allowable time step is proportional to the softened effect of the discretized model in an explicit analysis.

MID-FREQUENCY ACOUSTIC ANALYSIS USING EDGE-BASED SMOOTHED TETRAHEDRON RADIALPOINT INTERPOLATION METHODS

An edge-based smoothed tetrahedron radial point interpolation method (ES-T-RPIM) is formulated for the 3D acoustic problems, using the simplest tetrahedron mesh which is adaptive for any complicated geometry. In present ES-T-RPIM, the gradient smoothing operation is performed with respect to each edge-based smoothing domain, which is also serving as building blocks in the assembly of the stiffness matrix. The smoothed Galerkin weak form is then used to create the discretized system equations. The acoustic pressure is constructed using radial point interpolation method, and two typical schemes of selecting nodes for interpolation using RPIM have been introduced in detail. It turns out that the ES-T-RPIM provides an ideal amount of softening effect, and significantly reduces the numerical dispersion error in low- to mid-frequency range. Numerical examples demonstrate the superiority of the ES-T-RPIM for 3D acoustic analysis, especially at mid-frequency.

A Novel Alpha Gradient Smoothing Method (αGSM) for Fluid Problems

In this article, a novel alpha gradient smoothing method (αGSM) based on the strong form of governing equations for fluid problems is presented. The basic principle of αGSM is that the spatial derivatives at a location of interest are approximated by the gradient smoothing operation. The main difference among the piecewise-constant gradient smoothing method (PC-GSM), piecewise-linear gradient smoothing method (PL-GSM), and αGSM is the selection of smoothing function. In the αGSM, the α value controls the contribution of the PC-GSM and PL-GSM. The αGSM is also verified by the solving the Poisson equation. The proposed αGSM has been tested for one benchmark example. All the numerical results demonstrate that the αGSM is remarkably accurate, robust, and stable. Finally, the αGSM has been applied to analyze the flow characteristic in the diseased artery in terms of stenosis.

Smoothed finite element method for topology optimization involving incompressible materials

It is well known that the finite element method (FEM) suffers severely from the volumetric locking problem for incompressible materials in topology optimization owing to its numerical ‘overly stiff’ property. In this article, two typical smoothed FEMs with a certain softened effect, namely the node-based smoothed finite element method (NS-FEM) and the cell-based smoothed finite element method, are formulated to model the compressible and incompressible materials for topology optimization. Numerical examples have demonstrated that the NS-FEM with an ‘overly soft’ property is fairly effective in tackling the volumetric locking problem in topology optimization when both compressible and incompressible materials are involved.

Temperature effect on the performance of a dissipative dielectric elastomer generator with failure modes

Research on dielectric elastomer generators (DEGs) which can be utilized to convert mechanical energy to electrical energy has gained wide attention lately. However, very few works account for the operating temperature, viscoelasticity and current leakage in the analysis of DEGs simultaneously. In this study, under several compound four-stroke conversion cycles, the electromechanical performance and energy conversion of a dissipative DEG made of a very-high-bond (VHB) elastomer are investigated at different operating temperatures. The performance parameters such as energy density and conversion efficiency are calculated under different temperatures. Moreover, the common failure modes of the generator are considered: material rupture, loss of tension, electrical breakdown and electromechanical instability. The numerical results have distinctly shown that the operating temperature plays an important role in the performance of DEGs, which could possibly make a larger conversion efficiency for the DEG.

The artificial tree (AT) algorithm

Bionic intelligence algorithms have many advantages compared with traditional optimization algorithms. In this paper, inspired by the growth law of trees, a new bionic algorithm, named artificial tree (AT) algorithm is developed. In the proposed AT, the branch position is considered as the design variable. In addition, the branch is the solution, and the branch thickness is the indicator of the solution. The computing process of AT is achieved by simulating the transport of organic matters and the update of tree branches. The comparative analysis using thirty typical benchmark problems between AT algorithm and some well-known bionic intelligent methods is also performed. Based on numerical results, AT is found to be very effective in dealing with various problems. Display Omitted

Fundamental study of mechanism of band gap in fluid and solid/fluid phononic crystals

Abstract Phononic crystals (PCs) have possessed outstanding features to control/manipulate the propagation of the acoustic/sound wave. In this paper, the local resonant elements, such as local resonant cavity in fluid PCs and local resonant inclusion in solid/fluid PCs, are introduced. The effect of geometry parameters, Poissons ratio, Youngs modulus on the band gap solid/fluid PCs are investigated in detail. It is found that wider multiple band gaps are obtained for the fluid PCs with local resonant cavity of “+” hole compared with square and circle holes. More importantly, the very low-frequency band gaps can be obtained by introducing the local resonant inclusion with consideration of fluid-structural interaction for solid/fluid PCs. In addition, we have compared the sound transmission loss in fluid and solid/fluid PCs. The numerical results have clearly indicated that solid/fluids PCs with consideration of fluid-structural interaction can block the propagation of stress wave effectively compared with fluid PCs. The theoretical study and numerical simulation conducted in this work have provided a new avenue to design more innovative fluid and solid/fluid PCs.