Sandeep S. Pendhari

AN EFFICIENT SEMI-ANALYTICAL MODEL FOR COMPOSITE AND SANDWICH PLATES SUBJECTED TO THERMAL LOAD

A simple, semi-analytical model with mixed (stresses and displacements) fundamental variables starting from the exact three dimensional (3D) governing partial differential equations (PDEs) of laminated composite and sandwich plates for thermo-mechanical stress analysis has been presented in this paper. The plate is assumed simply supported on all four edges. Two different temperature variations through the thickness of plates are considered for numerical investigation. The accuracy and the effectiveness of the proposed model are assessed by comparing numerical results from the present investigation with the available elasticity solutions. Some new results for sandwich laminates are also presented for future reference.

On Accurate Stress Analysis of Composite and Sandwich Narrow Beams

A simple, semi-analytical methodology defining a two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) with mixed primary variables whose number equals the order of partial differential equations (PDEs) for narrow layered beams is proposed in this paper. These primary quantities consist of displacements ( u , w ) and the corresponding transverse stresses ( τ xz , σ z ). Continuity of transverse stresses and displacements through the thickness of a laminated beam is enforced naturally in the formulation. The accuracy and the effectiveness of the proposed methodology is addressed by comparing numerical results from the present formulation with available closed-form analytical and finite element (FE) solutions.

A New Partial Finite Element Model for Statics of Sandwich Plates

A new partial discretization formulation with four-noded bi-linear finite elements (FEs) has been developed in this study for flexural analysis of sandwich plates. Partial discretization results in solution of a two-point boundary value problem (BVP) governed by a system of coupled first-order ordinary differential equations (ODEs). Mixed degrees of freedom, displacements (u, v, w), and transverse stresses (τxz, τyz, σz) are the dependent variables and thus continuity of transverse stresses and displacements are implicitly enforced in the present formulation. Numerical investigations on symmetric and unsymmetric sandwich plates are performed and presented, involving both validation and solution of new problems.

Static Analysis of Functionally Graded Laminates According to Power-Law Variation of Elastic Modulus Under Bidirectional Bending

Three-dimensional static response of all-around simply supported functionally graded square/rectangular laminates is presented here based on higher order shear-normal (HOSNT) deformation theory and semi-analytical approach. Modulus of elasticity is assumed to be varied according to power law through the thickness of laminate and other material properties are assumed to be constant over the domain. Semi-analytical approach consists of defining two-point boundary value problem (BVP) in the thickness direction. It involves displacements and transverse stresses as primary degrees of freedoms (DOFs) and therefore, general stress boundary conditions can be applied on both top and bottom surface of laminate during the numerical solution. Whereas, in HOSNT, only displacements are considered as primary DOFs and Taylor’s series are used to expand primary DOFs through thickness direction which helps to take into account of transverse cross-sectional deformation modes. Minimum potential energy is used in HOSNT to der...

A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges

An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

A NEW PARTIAL DISCRETIZATION METHODOLOGY FOR NARROW COMPOSITE BEAMS UNDER PLANE STRESS CONDITIONS

A partial discretization formulation with two-noded finite elements (FEs) under plane stress conditions has been developed for flexural analysis of composite and sandwich beams subjected to transverse loading. The methodology consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) with four degrees of freedom (u, w, τxz and σz) per node. Continuity of interlaminar transverse stresses and displacements at laminae interfaces is implicitly enforced in the formulation. All the fundamental elasticity relationships between the components of stress, strain and displacement fields are explicitly maintained throughout the elastic continuum. Results have been obtained for cross-ply composite and sandwich beams. Excellent agreement with available analytical, mixed semianalytical and FE solutions is observed. Some new results with clamped support conditions have also been obtained and are presented to serve as benchmark solutions fo...