This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

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Electrodynamics Of Continuous Media

Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

Meshfree and particle methods and their applications

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Methods of Numerical Integration

The benzene-Xe (BXe) complex in its electronic ground state is studied using ab initio methods. Since this complex contains the heavy Xe atom, the relativistic effects cannot be neglected. We test two different approaches that describe the scalar relativistic effects in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations, used for the interaction energy calculations. The first one is based on the small core pseudopotential (PP), and the second one is based on the explicit treatment of scalar relativistic effects using the Douglas-Kroll-Hess (DKH) Hamiltonian. A few basis sets are tested with the PP and DKH, and for each one, the analytical potential energy surface (PES) is constructed. It is shown that the difference between PESs determined with PP and DKH methods is small, if the orbitals of the 4d subshell in Xe are correlated. We select the most appropriate approach for the calculation of the potential energy surface of BXe, with respect to accuracy and computational cost. The optimal level of theory includes a small Dunning's basis set for the benzene monomer and a larger PP basis set for Xe supplemented by midbond functions. The PES obtained using such an approach provides a reasonable accuracy when compared to the empirical one derived from the microwave spectra of BXe. The empirical and the theoretical values of intermolecular vibrational energies agree within 0.5 cm-1 up to second overtones. The vibrational energy level pattern of BXe is characterized by a distinct polyad structure.

Ab initio relativistic potential energy surfaces of benzene–Xe complex with application to intermolecular vibrations

Piezoelectric materials are the key element in various sensors and sensory devices used in industry and research. In this article, we use the meshless local Petrov–Galerkin method to analyze a thre...

Meshless analysis of piezoelectric sensor embedded in composite floor panel

This paper presents a computational method to analyze 2D crack problems in magneto-electro-elastic solid described by the gradient theory with the direct flexoelectric effect. The finite-element me...

Crack analysis in magneto-electro-elastic solids by gradient theory

The finite element method (FEM) is developed to analyse 2-D crack problems in piezoelectric solids that exhibit the size-effect. This phenomenon, which typically occurs in micro/nano electronic structures, is described by the strain- and electric field-gradients in the constitutive equations. The variational principle with the appropriate boundary conditions is employed to derive the governing equations, from which the FEM formulation with C1-continuous elements is developed and implemented. An example is presented to demonstrate the effects of the strain- and electric intensity-gradients on the electro-mechanical behavior of the cracked solid.

Vladimir Sladek

Papers

Ab initio relativistic potential energy surfaces of benzene–Xe complex with application to intermolecular vibrations

Meshless analysis of piezoelectric sensor embedded in composite floor panel

Crack analysis in magneto-electro-elastic solids by gradient theory

Flexoelectric effect for cracks in piezoelectric solids

Plate bending problems using the nonsingular boundary element formulation and C1-continuous elements