Zhenhan Yao

A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates

A new 4-node quadrilateral finite element is developed for the analysis of laminated composite plates containing distributed piezoelectric layers (surface bonded or embedded). The mechanical part of the element formulation is based on the first-order shear deformation theory. The formulation is established by generalizing that of the high performance Mindlin plate element ARS-Q12, which was derived based on the DKQ element formulation and Timoshenko’s beam theory. The layerwise linear theory is applied to deal with electric potential. Therefore, the number of electrical DOF is a variable depending on the number of plate sub-layers. Thus, there is no need to make any special assumptions with regards to the through-thickness variation of the electric potential, which is the true situation. Furthermore, a new “partial hybrid”-enhanced procedure is presented to improve the stresses solutions, especially for the calculation of transverse shear stresses. The proposed element, denoted as CTMQE, is free of shear locking and it exhibits excellent capability in the analysis of thin to moderately thick piezoelectric laminated composite plates.

Effective elastic properties of 2-D solids with circular holes: numerical simulations

In order to evaluate the reliability and precision of the existing approximate micromechanically-based theoretical schemes for the prediction of the effective elastic properties of a sheet containing holes, numerical simulations have been carried out. The boundary-element method has been adopted in numerical simulations on account of its numerical precision and other remarkable merits. First, the relationships between effective elastic properties of 2-D solids with random circular holes and the volume fraction of holes have been studied. Furthermore, to investigate the influence of the interaction between holes on the effective material moduli of 2-D solids, another kind of model with normally distributed holes has been analyzed. By comparing computational results with the theoretical solutions, the presently existing theoretical methods have been comprehensively evaluated. Furthermore, the effects of two parameters in the normal distribution function on the effective material moduli have been investigated in detail.

A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates

A simple displacement-based, quadrilateral 20 DOF (5 DOF per node) bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented in this paper. This element is constructed by the following procedure: (i) the variation functions of the rotation and the shear strain along each side of the element are determined using Timoshenkos beam theory; and (ii) the shear strain, rotation and in-plane displacement fields in the domain of the element are then determined using the technique of improved interpolation. Furthermore, a simple hybrid procedure is also proposed to improve the stress solutions. The proposed element, denoted as CTMQ20, possesses the advantages of both the displacement-based and hybrid elements. Thus, excellent results for both displacements and stresses, especially for the transverse shear stresses, can be obtained.

FM-BEM evaluation for effective elastic moduli of microcracked solids

A fast multipole boundary element method (FM-BEM) was applied for the analysis of microcracked solids. Both the computational complexity and memory requirement are reduced to O(N), where N is the number of degrees of freedom. The effective elastic moduli of a 2-D solid containing thousands of randomly distributed microcracks were evaluated using the FM-BEM. The results prove that both the differential method and the method proposed by Feng and Yu provide satisfactory estimates to such problems. The effect of a non-uniform distribution of microcracks has been studied using a novel model. The numerical results show that the non-uniform distribution induces a small increase in the global stiffness.

Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches

The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and traction boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straight-forward derivations of weakly singular traction BIEs for solids undergoing small deformations are also presented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the present methods are very promising, especially for solving the elastic problems in which the singularities in displacements, strains, and stresses are of primary concern.

Identification of the material parameters of laminated plates

A scheme is developed to identify the material parameters of laminated plates using mathematical optimization and measured eigenfrequencies of the object. The object function of the optimization is defined as the difference between the measured frequencies and the computed frequencies of the laminated plates. The sensitivity of the structural eigenvalue with respect to the material parameters is analyzed. A numerical example is presented to show the feasibility of the scheme.