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The prediction of the response of reinforced concrete structures subjected to projectiles impact still presents open questions. These include the rate dependence of material properties, the interaction between concrete and steel reinforcement and the simulation of fracture and fragmentation. Because the appearance of discontinuities in the target structure is difficult to account using a continuum approach, the application of discrete models was developed as an appealing alternative. A version of the discrete model in which nodal masses are linked by an array of uniaxial elements, herein called discrete element method, is used in this study. This method was implemented in the system Abaqus to take advantage of its numerical and post-processing capabilities. A reinforced concrete rectangular plate subjected to impact of a projectile is examined in detail. Comparisons between experimental and numerical results are shown with the aim of validating the proposed method.

A mixed semi-analytical computational model is presented which accounts for the coupled electrical, mechanical and thermal response of layered piezoelectric finitely long hollow circular cylinders. Boundary value problem (BVP) of an axisymmetric cylinder is considered here as a two-dimensional plane strain problem in the (r, z) plane, which is based on the exact theory of elasticity. After assuming diaphragm-supported end conditions in the longitudinal (z) direction, the resulting mathematical model is cast in the form of first-order simultaneous ordinary differential equations which are integrated through an effective numerical integration technique by first transforming the BVP into a set of initial value problems. New results of finite length cylinders are generated and presented for future reference.

A two-point boundary value problem (BVP) is formed in the present work governed by a set of first-order coupled ordinary differential equations (ODEs) in terms of displacements and the transverse stresses through the thickness of laminate (in domain -h/2 < z < h/2) by introducing partial discretization methodology only in the plan area of the three dimensional (3D) laminate. The primary dependent variables in the ODEs are those which occur naturally on a plane z=a constant. An effective numerical integration (NI) technique is utilized for tackling the two-point BVP in an efficient manner. Numerical studies on cross-ply and angle-ply composite plates are performed and presented, involving both validation and solution of new problems.

A refined higher-order shear deformation theory has been developed for large amplitude, in die sense of von Karman, free vibration analysis of fibre reinforced cross-ply composite and sandwich laminates by assuming cubic variations of in-plane displacement components and a constant transverse displacement component through the thickness of the laminate. The theory accounts for warping of the transverse cross-section, which cannot be modelled with the Reissner-Mindlin first-order shear deformation theory. The displacement-based finite element method of analysis using C0 isoparametric nine-node quadrilateral elements of the Lagrangian family is adopted. A special mass matrix diagonalization scheme is employed which conserves the total mass of the element and includes the effects due to rotary inertia terms. The validity and efficiency of the present development is then established by obtaining the solutions to a wide range of problems and comparing them with the available two- and three-dimensional closed-form and finite element solutions. Some new results are also generated in a non-linear context for future comparisons.

An explicitly through the thickness integrated two-dimensional version of the three-dimensional degenerated shell element is formulated here to study the dynamics of elastic shells. A nine-noded quadrilateral Lagrangian element is used with five degrees of freedom per node. A specialized mass diagonalization scheme, developed by Hinton, Rock and Zienkiewicz, is used which conserves the total mass of the element and also includes the effects of the rotary inertia terms. Hamilton's principle is used to derive the equations of motion. Mode superposition coupled with Duhamel's integral is first employed to obtain a solution of the equations of motion in time. Mode shapes and frequencies are computed by subspace iteration technique. Direct time integration using the implicit Newmark-beta method is also carried out. Several examples are presented and the results obtained by mode superposition and direct time integration methods are compared.

In this paper, a new set of higher order theories for the analysis of composite and sandwich beams by using C0 finite elements is presented. These theories incorporate the more realistic non-linear variation of displacements through the beam thickness, thus eliminating the use of shear correction coefficients. Discrete Lagrangian four-noded cubic element models having five, six and seven degrees of freedom per node are used. The computer program developed incorporates the realistic prediction of interlaminar stresses from equilibrium equations. By comparing the results obtained with the elasticity solution and the classical plate theory, it is shown that the present higher order theories give a much better approximation to the behaviour of thick to thin laminated composite beams. Numerical results for unsymmetric sandwich beams are also presented for future reference.

An attempt has been made to study the effect of cross-sectional warping in the symmetrically laminated anisotropic composite sandwich plates for transient loads. A higher-order shear deformation theory (HOST) is used in conjunction with the simple displacement based C0 finite element method (FEM). As is well-known, the classical first-order theories hitherto considered were inadequate to describe the propagation of waves in the highly orthotropic sandwich laminates. The present theory, which is more accurate than the Reissner-Mindlin theory, is applied herein, for the evaluation of plate response to different types of dynamic loads. An explicit central difference scheme is employed for the integration of dynamic equations of equilibrium with a diagonalized mass matrix obtained by a special procedure applicable to quadrilateral isoparametric elements. The numerical results of the present investigation have been compared with the first-order shear deformation theory (FOST) and the differences between HOST and FOST are examined. The results presented here should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results.

A refined shell theory has been developed for the analysis of isotropic, orthotropic and anisotropic fibre-reinforced laminated composite and sandwich shells. This theory is based on a higher-order displacement model and the three-dimensional Hooke's laws for shell material, giving rise to a more realistic representation of the cross-sectional deformation. The superparametric shell element with four-noded linear eight/nine-noded quadratic and twelve/sixteen-noded cubic, serendipity/Lagrangian shape functions can be employed. In addition to the present higher-order shear deformation shell theory (HOST), a first-order shear deformation shell theory (FOST), following Reissner-Mindlin plate's formulation, is developed and the results are compared with the closed-form solutions (CFS). The parametric effects of the finite element mesh, radius-to-arc length ratio, arc length-to-thickness ratio, lamination scheme, Gaussian integration rule, and material anisotropy on the response of the laminated composite shells are investigated. Results are tabulated to provide an easy means for future comparisons by other investigators.

Impact responses of composite laminates are investigated with C0 finite elements. A ninenode isoparametric quadrilateral element based on a higher-order theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the explicit central difference technique is used in conjunction with the special mass matrix diagonalization scheme. Numerical results, including the contact force histories, deflections and strains in the plate, are presented.

Discrete methods for practical coupled three-dimensional fluid-structure interaction problems are developed. A C0 explicity integrated two-dimensional degenerate shell element and a three-dimensional fluid element are coupled to study shell dynamics, fluid transient and coupled shell-fluid interaction problems. The method of partitioning is used to integrate the fluid and shell meshes in a staggered fashion in an optimum manner. Effective explicit-implicit partitioning is shown to achieve high computational efficiency for this type of problem.