This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

A critical review of recent research on functionally graded plates

The review outlines modern trends in theoretical developments, novel designs and modern applications of sandwich structures. The most recent work published at the time of writing of this review is considered, older sources are listed only on as-needed basis. The review begins with the discussion on the analytical models and methods of analysis of sandwich structures as well as representative problems utilizing or comparing these models. Novel designs of sandwich structures is further elucidated concentrating on miscellaneous cores, introduction of nanotubes and smart materials in the elements of a sandwich structure as well as using functionally graded designs. Examples of problems experienced by developers and designers of sandwich structures, including typical damage, response under miscellaneous loads, environmental effects and fire are considered. Sample applications of sandwich structures included in the review concentrate on aerospace, civil and marine engineering, electronics and biomedical areas. Finally, the authors suggest a list of areas where they envision a pressing need in further research.

Review of current trends in research and applications of sandwich structures

In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

INTRODUCTION TO COMPOSITE MATERIALS Chapter Objectives Introduction Classi?cation Recycling Fiber-Reinforced Composites Mechanics Terminology Summary Key Terms Exercise Set References MACROMECHANICAL ANALYSIS OF A LAMINA Chapter Objectives Introduction Review of De?nitions Hooke's Law for Different Types of Materials Hooke's Law for a Two-Dimensional Unidirectional Lamina Hooke's Law for a Two-Dimensional Angle Lamina Engineering Constants of an Angle Lamina Invariant Form of Stiffness and Compliance Matrices for an Angle Lamina Strength Failure Theories of an Angle Lamina Hygrothermal Stresses and Strains in a Lamina Summary Key Terms Exercise Set References APPENDIX A: MATRIX ALGEBRA Key Terms APPENDIX B: TRANSFORMATION OF STRESSES AND STRAINS Transformation of Stress Transformation of Strains Key Terms MICROMECHANICAL ANALYSIS OF A LAMINA Chapter Objectives Introduction Volume and Mass Fractions, Density, and Void Content Evaluation of the Four Elastic Moduli Ultimate Strengths of a Unidirectional Lamina Coefficients of Thermal Expansion Coefficients of Moisture Expansion Summary Key Terms Exercise Set References MACROMECHANICAL ANALYSIS OF LAMINATES Chapter Objectives Introduction Laminate Code Stress-Strain Relations for a Laminate In-Plane and Flexural Modulus of a Laminate Hygrothermal Effects in a Laminate Summary Key Terms Exercise Set References FAILURE, ANALYSIS, AND DESIGN OF LAMINATES Chapter Objectives Introduction Special Cases of Laminates Failure Criterion for a Laminate Design of a Laminated Composite Other Mechanical Design Issues Summary Key Terms Exercise Set References BENDING OF BEAMS Chapter Objectives Introduction Symmetric Beams Nonsymmetric Beams Summary Key Terms Exercise Set References INDEX

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Mechanics of composite materials

Composites exhibit a considerable amount of variation in their material properties because their fabrication/manufacturing process involves a large number of parameters that cannot be controlled effectively. In the present study, the material properties have been modeled as random variables for better prediction of the system behavior. The classical laminate theory and first-order and higher-order shear deformation theories have been employed in deriving the governing equations for buckling of laminated rectangular plates. A mean-centered first-order perturbation technique has been used to find the second-order statistics of the buckling load. The approach has been validated by comparison with results of Monte Carlo simulation. Typical results have been presented for a plate with all edges simply supported. The effectiveness of the theories in predicting the buckling load dispersions has been examined. The sensitivity of buckling loads to change in the standard deviation of random material properties and ...

Bhrigu Nath Singh

Papers

Effects of random material properties on buckling of composite plates

Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM

Stochastic perturbation-based finite element for deflection statistics of soft core sandwich plate with random material properties

Post buckling response of laminated composite plate on elastic foundation with random system properties

Buckling and post-buckling of laminated composite plates