T. Nguyen-Thoi

An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures

An edge-based smoothed finite element method (ES-FEM) was recently proposed to significantly improve the accuracy and convergence rate of the standard finite element method for static, free and forced vibration analyses of solids using three-node triangular elements that can be generated automatically for complicated geometries. In this work, it is further extended to static and eigenvalue analyses of two-dimensional piezoelectric structures. In the present ES-FEM, the approximation of the displacement and electric potential fields is the same as in the standard linear FEM, while mechanical strains and electric fields are smoothed over the smoothing domains associated with the edges of the triangles. The system stiffness matrix is then computed via a simple summation over these smoothed domains. The results of several numerical examples show that: (1) the ES-FEM is in a good agreement with the analytical solutions as well as experimental ones and (2) the ES-FEM is much more accurate than the linear triangular elements (T3) and often found to be even more accurate than the FEM using quadrilateral elements (Q4) when the same sets of nodes are used.

Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3)

The cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular elements was recently proposed to improve the performance of the discrete shear gap method (DSG3) for static and free vibration analyses of isotropic Mindlin plates. In this paper, the CS-FEM-DSG3 is further extended for static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators. In the piezoelectric composite plates, the electric potential is assumed to be a linear function through the thickness of each piezoelectric sublayer. A displacement and velocity feedback control algorithm is used for active control of the static deflection and the dynamic response of the plates through closed loop control with bonded or embedded distributed piezoelectric sensors and actuators. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of other available numerical results.

ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS

A node-based smoothed finite element method (NS-FEM) for solving solid mechanics problems using a mesh of general polygonal elements was recently proposed. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh, and a number of important properties have been found, such as the upper bound property and free from the volumetric locking. The examination was performed only for two-dimensional (2D) problems. In this paper, we (1) extend the NS-FEM to three-dimensional (3D) problems using tetrahedral elements (NS-FEM-T4), (2) reconfirm the upper bound and free from the volumetric locking properties for 3D problems, and (3) explore further other properties of NS-FEM for both 2D and 3D problems. In addition, our examinations will be thorough and performed fully using the error norms in both energy and displacement. The results in this work revealed that NS-FEM possesses two additional interesting properties that quite simi...

AN EDGE-BASED SMOOTHED FINITE ELEMENT METHOD FOR ANALYSIS OF LAMINATED COMPOSITE PLATES

This paper promotes a novel numerical approach to static, free vibration and buckling analyses of laminated composite plates by an edge-based smoothed finite method (ES-FEM). In the present ES-FEM formulation, the system stiffness matrix is established by using the strain smoothing technique over the smoothing domains associated with the edges of the triangular elements. A discrete shear gap (DSG3) technique without shear locking is combined into the ES-FEM to give a so-called edge-based smoothed discrete shear gap method (ES-DSG3) for analysis of laminated composite plates. The present method uses only linear interpolations and its implementation into finite element programs is quite simple. Numerical results for analysis of laminated composite plates show that the ES-DSG3 performs quite well compared to several other published approaches in the literature.

FREE AND FORCED VIBRATION ANALYSIS USING THE n-SIDED POLYGONAL CELL-BASED SMOOTHED FINITE ELEMENT METHOD (nCS-FEM)

A n-sided polygonal cell-based smoothed finite element method (nCS-FEM) was recently proposed to analyze the elastic solid mechanics problems, in which the problem domain can be discretized by a set of polygons with an arbitrary number of sides. In this paper, the nCS-FEM is further extended to the free and forced vibration analyses of two-dimensional (2D) dynamic problems. A simple lump mass matrix is proposed and hence the complicated integrations related to computing the consistent mass matrix can be avoided in the nCS-FEM. Several numerical examples are investigated and the results found of the nCS-FEM agree well with exact solutions and with those of others FEM.

AN APPLICATION OF THE ES-FEM IN SOLID DOMAIN FOR DYNAMIC ANALYSIS OF 2D FLUID–SOLID INTERACTION PROBLEMS

An edge-based smoothed finite element method (ES-FEM-T3) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics analyses. In this paper, the ES-FEM-T3 is further extended to the dynamic analysis of 2D fluid–solid interaction problems based on the pressure-displacement formulation. In the present coupled method, both solid and fluid domain is discretized by triangular elements. In the fluid domain, the standard FEM is used, while in the solid domain, we use the ES-FEM-T3 in which the gradient smoothing technique based on the smoothing domains associated with the edges of triangles is used to smooth the gradient of displacement. This gradient smoothing technique can provide proper softening effect, and thus improve significantly the solution of coupled system. Some numerical examples have been presented to illustrate the effectiveness of the proposed coupled method compared with some existing methods for 2D fluid–solid interaction problems.

An improved constrained differential evolution using discrete variables (D-ICDE) for layout optimization of truss structures

A discrete variable technique is integrated into ICDE to give Discrete-ICDE.Discrete-ICDE is then applied for the truss layout optimization problems.Numerical results show that Discrete-ICDE is robust, effective and reliable. Recently, an improved (µ+λ) constrainted differential evolution (ICDE) has been proposed and proven to be robust and effective for solving constrainted optimization problems. However, so far, the ICDE has been developed mainly for continuous design variables, and hence it becomes inappropriate for solving layout truss optimization problems which contain both discrete and continuous variables. This paper hence fills this gap by proposing a novel discrete variables handling technique and integrating it into original ICDE to give a so-called Discrete-ICDE (D-ICDE) for solving layout truss optimization problems. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress, displacement and buckling limitations. Numerical examples of five classical truss problems are carried out and compared to other state-of-the-art optimization methods to illustrate the reliability and effectiveness of the proposed method. The D-ICDEs performance shows that it not only successfully handles discrete variables but also significantly improves the convergence of layout truss optimization problem. The D-ICDE is promising to extend for determining the optimal solution of other structural optimization problems which contain both discrete and continuous variables.

COMPUTATION OF LIMIT LOAD USING EDGE-BASED SMOOTHED FINITE ELEMENT METHOD AND SECOND-ORDER CONE PROGRAMMING

This paper presents a novel numerical procedure for limit analysis of plane problems using edge-based smoothed finite element method (ES-FEM) in combination with second-order cone programming. In the ES-FEM, the discrete weak form is obtained based on the strain smoothing technique over smoothing domains associated with the edges of the elements. Using constant smoothing functions, the incompressibility condition only needs to be enforced at one point in each smoothing domain, and only one Gaussian point is required, ensuring that the size of the resulting optimization problem is kept to a minimum. The discretization problem is transformed into the form of a second-order cone programming problem which can be solved using highly efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plane stress and strain problems.

An Edge-Based Smoothed Discrete Shear Gap Method Using the C0-Type Higher-Order Shear Deformation Theory for Analysis of Laminated Composite Plates

The edge-based smoothing discrete shear gap method (ES-DSG3) using three-node triangular elements is combined with a C0-type higher-order shear deformation theory (HSDT) to give a new linear triangular plate element for static, free vibration, and buckling analyses of laminated composite plates. In the ES-DSG3, only the linear approximation is necessary, and the discrete shear gap method (DSG) for triangular plate elements is used to avoid the shear locking and spurious zero energy modes. In addition, the stiffness matrices are calculated relying on smoothing domains associated with the edges of the triangular elements through an edge-based strain smoothing technique. Using the C0-type HSDT, the shear correction factors in the original ES-DSG3 can be removed and replaced by two additional degrees of freedom at each node. The numerical examples demonstrated that the ES-DSG3 show remarkably excellent performance compared to several other published elements in the literature.

An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures

ICDE is extended to the RBDO problem of truss structures by combining ICDE with SORA which gives a so-called the SORA-ICDE.In SORA-ICDE, the optimization loop and reliability assessment loop are decoupled, and hence the efficiency in solving RBDO problems is ensured and improved significantly.Numerical results for five benchmark problems illustrate the effectiveness of the SORA-ICDE in solving the RBDO problem of truss structures. Recently, a Sequential Optimization and Reliability Assessment (SORA) method was proposed and proven to be effective for solving reliability-based design optimization (RBDO) problems. In the SORA, the optimization loop and the reliability assessment loop are decoupled from each other. This helps improve the efficiency of the SORA significantly. However, the SORA still exists two main drawbacks: (1) the optimal solutions are easily trapped within local extremes and (2) the optimal results depend on the initial trial points. To overcome these drawbacks, this paper integrates the SORA with the Improved Constrained Differential Evolution algorithm (ICDE) to give a so-called SORA-ICDE for solving RBDO problems. Due to the global search mechanism, the SORA-ICDE can easily obtain global solutions regardless of initial points. The numerical results obtained in the paper are compared with available results in the literature to illustrate the efficiency, applicability and precision of the SORA-ICDE in solving the RBDO problems for truss structures.