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Elasticity Solutions (elasticity + solution)
Selected AbstractsStress analyses of laminates under cylindrical bendingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Tarun Kant Abstract A semi-analytical approach for evaluation of stresses and displacements in composite and sandwich laminates under cylindrical bending subjected to transverse load has been developed in this paper. Two dimensional (2D) partial differential equations (PDEs) of such a laminate are obtained by imposing plane-strain conditions of elasticity. The fundamental dependent variables are so selected in this formulation that they satisfy the continuity of displacements and transverse interlaminar stresses at the laminate interface through the thickness. The set of governing PDEs are transformed into a set of coupled first-order ordinary differential equations (ODEs) in thickness direction by assuming suitable global orthogonal trigonometric functions for the fundamental variables satisfying the boundary conditions. These ODEs are numerically integrated by a specially formulated ODE integrator algorithm involving transformation of a two-point boundary value problem (BVP) into a set of initial value problems (IVPs). Numerical studies on both composite and sandwich laminates for various aspect ratios are performed and presented. Accuracy of the present approach is demonstrated by comparing the results with the available elasticity solution. It is seen that the present results are in excellent agreement with the elasticity solutions. Some new results for sandwich laminates and for uniform loading condition are presented for future reference. Copyright © 2006 John Wiley & Sons, Ltd. [source] Improving the efficiency of finite element formulations in laminated compositesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2002Kostas P. Soldatos Abstract This communication extends the principles of an advanced smeared laminate plate theory towards the development of corresponding FE models and codes. The present FE numerical results are compared with those based on exact elasticity solutions, as well as those of corresponding FE models based on three conventional laminate plate theories. These comparisons show that, compared to those conventional FE codes, the proposed FE formulation that uses also a small and fixed number of nodal degrees of freedom improves substantially the accuracy of stress predictions. They also show that the present numerical results are particularly accurate even for very thick laminates. Copyright © 2002 John Wiley & Sons, Ltd. [source] Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Jun-Sik Kim Abstract A finite element based on the efficient higher-order zig-zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig-zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig-zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher-order zig-zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three-dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||