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

Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams

Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

The nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Karman type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams.

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Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core

Corrigendum to "Free vibration of higher-order sandwich and composite arches, Part I: Formulation" [J. Sound Vib. 310 (1-2) (2008) 91-109]

Erratum to 'Transient dynamic analysis of higher order sandwich and composite arches' (Compos Struct 93 (2011) 1201-1216)

https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29EM.1943-7889.0000305

Erratum for “On the Flexural Analysis of Sandwich and Composite Arches through an Isoparametric Higher-Order Model” by Sudhakar R. Marur and Tarun Kant

Hybrid ‘Thermoplastics and Steel’ Bumper Beam Solution to Protect the Vehicle in Low Speed Crashes

In an embodiment, a method of absorbing energy comprises: impacting a portion of a vehicle comprising a coil energy absorber, and compressing and plastically deforming the coil energy absorber. The coil energy absorber has an initial height and is located between the support structure and the covering, and wherein the coil energy absorber absorbs energy upon impact such that, after the impact, the coil energy absorber has a final height that is less than or equal to 90% of the initial height. The coil energy absorber is made of plastic. The coil energy absorber is located between a fascia and a support structure of the vehicle.

Sudhakar Ramamoorthy Marur

Papers

Corrigendum to "Free vibration of higher-order sandwich and composite arches, Part I: Formulation" [J. Sound Vib. 310 (1-2) (2008) 91-109]

Erratum to 'Transient dynamic analysis of higher order sandwich and composite arches' (Compos Struct 93 (2011) 1201-1216)

Erratum for “On the Flexural Analysis of Sandwich and Composite Arches through an Isoparametric Higher-Order Model” by Sudhakar R. Marur and Tarun Kant

Hybrid ‘Thermoplastics and Steel’ Bumper Beam Solution to Protect the Vehicle in Low Speed Crashes

Methods for making and using plastically deformable coil energy management systems