During the past several years, groundwater has become a subject of great concern to the public. Unfortunately, this attention is the result of many serious subsurface pollution problems. The need to manage or clean up these pollution aquifers has created a great demand for methods or tools to accurately predict groundwater flow and pollutant transport, and how they will change in response to imposed stresses. Bear and Verruijt (p. xi) state, “The necessary information about the response of the system is provided by a model that describes the behavior of the considered system in response to excitation.”

Modeling Groundwater Flow and Pollution

Free vibration analysis for plates with arbitrary boundary conditions using a novel spectral-dynamic stiffness method

Engineering applications in conventional numerical modeling are investigated by domain decomposition techniques because, generally, structural components do not have a regular shape. The most common and versatile numerical approach, in this regard, is the Finite Element (FE) method, which uses low order polynomials and the variational formulation for the solution of the differential problem. In contrast with the classic approach, the present paper shows a strong form collocation method for solving laminated composite plates wherein discontinuities arise. Both approaches need mapping technique for converting arbitrarily shaped elements into the computational space. Since the present strong form technique can deal with variable order approximating polynomials within each element, advanced blending function mapping must be employed for treating any discontinuity and distortion effect using the smallest number of elements. The Differential Quadrature (DQ) method is utilized for solving the mathematical problem and isogeometric mapping is implemented for the nonlinear mapping of complex shapes. The present methodology belongs to the framework of Isogeometric Analysis (IGA), therefore this approach is termed Strong Formulation Isogeometric Analysis (SFIGA). Numerical applications show the accuracy, stability and reliability of the present methodology.

Strong Formulation Isogeometric Analysis (SFIGA) for laminated composite arbitrarily shaped plates

An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part I: Theory

Summary
In the present paper, strong form finite elements are employed for the free vibration study of laminated arbitrarily shaped plates. In particular, the stability and accuracy of three different Fourier expansion-based differential quadrature techniques are shown. These techniques are used to solve the partial differential system of equations inside each computational element. The three approaches are called harmonic differential quadrature, Fourier differential quadrature and improved Fourier expansion-based differential quadrature methods. The improved Fourier expansion-based differential quadrature method implements auxiliary functions in order to approximate functional derivatives up to the fourth order, with respect to the Fourier differential quadrature method that has a basis made of sines and cosines. All the present applications are related to literature comparisons and the presentation of new results for further investigation within the same topic. A study of such kind has never been proposed in the literature, and it could be useful as a reference for future investigation in this matter. Copyright © 2016 John Wiley & Sons, Ltd.

Xiang Liu

Papers

Free vibration analysis for plates with arbitrary boundary conditions using a novel spectral-dynamic stiffness method

An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part I: Theory

Mechanical properties of Nomex honeycomb sandwich panels under dynamic impact

Dynamic stiffness matrix of a rectangular plate for the general case

Sensitivity and dynamic analysis of train-bridge coupled system with multiple random factors