: An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

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Virtual crack closure technique: History, approach, and applications

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

Review of State of Art of Smart Structures and Integrated Systems

A review of theories for the modeling and analysis of functionally graded plates and shells

Characterization and analysis of delamination fracture in composites: An overview of developments from 1990 to 2001

Vibration characteristics of functionally graded cylindrical shells under various boundary conditions

Nonlocal elasticity theory is a growing technique for the mechanical analyses of microelectromechanical (MEMS) and nanoelectromechanical (NEMS) based structures. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as single-walled carbon nanotubes (SWCNTs). In this article, nonlocal elasticity and Timoshenko beam theory are implemented to study the vibration response of SWCNT embedded in an elastic medium. Influence of the surrounding elastic medium on the fundamental frequencies of the SWCNT is investigated. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of the SWCNT with the surrounding elastic medium. A differential quadrature approach is being utilized and numerical solutions for the natural frequencies are obtained. Influences of nonlocal effects, Winkler modulus parameter, Pasternak shear modulus parameter, and aspect ratio on the frequency of SWCNT are analyzed and discussed. The present study illustr...

Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

In this paper, first-order shear deformation theory (FSDT) is employed to study vibration control of laminated composite plates. The magnetostrictive layers are used to control and enhance the vibration suppression via velocity feedback with a constant gain distributed control. Analytical solutions of the equations governing laminated plates with embedded magnetostrictive layers are obtained for simply-supported boundary conditions. The effects of material properties, lamination scheme, and placement of magnetostrictive layers with respect to laminate midplane on vibration suppression are studied in detail.

Control of laminated composite plates using magnetostrictive layers

In this paper structural analysis of nonhomogeneous nanotubes has been carried out using nonlocal elasticity theory. Governing differential equations of nonhomogeneous nanotubes are derived. Nanotubes include both single wall nanotube (SWNT) and double wall nanotube (DWNT). Nonlocal theory of elasticity has been employed to include the scale effect of the nanotubes. Nonlocal parameter, elastic modulus, density and diameter of the cross section are assumed to be functions of spatial coordinates. General Differential Quadrature (GDQ) method has been employed to solve the governing differential equations of the nanotubes. Various boundary conditions have been applied to the nanotubes. Present results considering nonlocal theory are in good agreement with the results available in the
literature. Effect of variation of various geometrical and material parameters on the structural response of the nonhomogeneous nanotubes has been investigated. Present results of the nonhomogeneous nanotubes are useful in the design of the nanotubes.

Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory

In the present paper, to analyse the vibration, buckling and bending of carbon nanotubes computations are carried out employing finite element formulation. Present analysis includes nonlocal Timoshenko beam theory and sensitivity of thermal environment. Governing differential equations are derived for the analyses of structural response of carbon nanotubes. Employing MATLAB code the linear algebraic equations are solved. Structural responses of carbon nanotubes are studied. Convergence study of the finite element formulation has been performed. Thermal effects on carbon nanotubes responses have been investigated based on nonlocal and thermal elasticity. Influences of (i) carbon nanotubes geometrical properties like length, diameter and thickness, (ii) nonlocal parameter and (iii) environmental temperature change on the structural response of the carbon nanotubes are studied.

S. C. Pradhan

Papers

Vibration characteristics of functionally graded cylindrical shells under various boundary conditions

Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

Control of laminated composite plates using magnetostrictive layers

Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory

Finite element analysis of CNTs based on nonlocal elasticity and Timoshenko beam theory including thermal effect