Department of Mechanical Engineering

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Browsing Department of Mechanical Engineering by Subject "3D Analytical Solution"

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    Three-Dimensional analytical solutions for static and Modal Analysis of Piezolaminated Cylindrical Shells using Extended Kantorovich Method
    (2022) Kar, Shranish
    The recent smart structures have extensive applications which needs to be analysed through the integration of multi-physics based governing theories. The multi-field responses of the structures are truly three-dimensional (3D) in nature which can be accurately predicted only through the application of 3D theories. Presently, a semi-analytical solution based on the multi-term extended Kantorovich method (EKM) has been developed. For the first time, the method has been extended to obtain 3D elasticity/ piezoelasticity based solution for the static and free vibration analysis of hybrid laminated composite cylindrical shells. Its ability to solve for cylindrical shells with any/ arbitrary combinations of support conditions such as simply supported, clamped and free edges is a notable feature. Derivation of the weak form of governing equations from a Reissner’s-type mixed variational principle, inclusion of fully coupled constitutive relation, shear-slip phenomena, multi-term and multi-field variable incorporation in the formulation are some of the novelty in the presently developed solution. The weak form of the governing equations are obtained from the mixed type variational principle where displacements, stresses, and electrical field variables are all treated as the primary variables. Subsequently, the expression for multi-term EKM in terms of separable functions of the coordinates θ and r, is substituted in the variational equation to obtain two systems of non-homogeneous ordinary differential equations (ODE)s in θ and r. The system of ODEs in r contains variable coefficients whose solution is obtained through a modified power series, whereas the system of ODEs in θ contains constant coefficients which are solved in closed-form through iterations. An extensive numerical study of cross-ply, angle-ply, sandwich laminates, shallow, deep, thin, moderately thick and thick cylindrical shell panels have been conducted. The effects of these parameters and arbitrary boundary conditions has been investigated. The nature of stresses at the clamped edges, boundary effects, interfacial discontinuities and deflection extremities are accurately predicted where the inconsistencies in 3D finite element (FE) results have been observed, otherwise.