In this study, a simple C
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isoparametric finite element formulation based on higher-order shear deformation theory is presented for static analysis of functionally graded material sandwich shells ...(FGMSS). To characterize the membrane-flexure behavior observed in a functionally graded shell, a displacement field involving higher-order terms in in-plane and transverse fields is considered. The proposed kinematics field incorporates for transverse normal deformation, transverse shear deformation, and nonlinear variation of the in-plane displacement field through the thickness to predict the overall response of the shell in an accurate sense. To develop the efficient C
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formulation, the derivatives of transverse displacement are treated as independent field variables (nodal unknowns). Voigt's rule of mixture is employed to ascertain the mechanical properties of each layer's constituents along the thickness direction. A wide range of numerical problems are solved assuming various parameters: side-thickness ratio, curvature-side ratio, and gradation parameter, and their interactions with regard to static analysis of FGMSS are discussed in brief. Deflection and stresses incorporating different thickness schemes of sandwich shells are presented in the form of figures. To validate the results, a functionally graded shell without sandwich arrangement is considered. Since no results are available on static analysis of FGMSS, the present 2D model based on the finite element method might be helpful in assessing the applicability of other analytical and numerical models in this area in the future.
The objective of this work is to propose a simple efficient finite element, based on Reddy’s third-order shear deformation theory, for analyzing the bending behavior of isotropic and composite ...laminated plates. It is a 2D isoparametric quadrilateral C
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four-node element with seven degrees of freedom at each node, three translation components, two rotations, and two higher-order rotational degrees. A selective numerical integration technique is introduced for the numerical formulation in order to improve results and to alleviate the locking problem. The formulation is able to take into account the parabolic distribution of transverse shear across the plate thickness in the bending behavior of isotropic and laminated composite plates, both thin and thick, without a need for correction factors. The performance and reliability of the formulation proposed are confirmed by comparing the author’s results with those obtained using the 3D elasticity theory, analytical solutions, and other advanced finite-element models.
An identification algorithm based on an isoparametric graded finite element model is developed to identify the material parameters of the plane structure of functionally graded materials (FGMs). The ...material parameter identification problem is formulated as the problem of minimizing the objective function, which is defined as a square sum of differences between measured displacement and calculated displacement by the isoparametric graded finite element approach. The minimization problem is solved by using the Levenberg-Marquardt method, in which the sensitivity calculation is based on the differentiation of the governing equations of the isoparametric graded finite element model. The validity of this algorithm is illustrated by some numerical experiments. The numerical results reveal that the proposed algorithm not only has high accuracy and stable convergence, but is also robust to the effects of measured displacement noise.
Tuned liquid column damper (TLCD) is a kind of passive damper that use water sloshing motion to control structural vibration in tall buildings, wind turbines and ships. This paper presents finite ...element analysis of sloshing in 2D water tank using a pressure based Eulerian approach. The fluid domain is discretised by an isoparametric quadrilateral finite element. The cavity was modelled with rigid contours and free surface in order to study the decoupled liquid reservoir. Next, the cavity was coupled to a flexible structure with free vibration and forced vibration. The numerical results obtained by the created program were validated using experimental results 1 presenting acceptable errors with less than 5k elements.
The design of high-performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. Understanding the behavior of perforated laminates is ...necessary for structural design. In the current work, stress concentrations taking place in laminated and isotropic plates subjected to tensile load are investigated. The stress concentrations are obtained using a recent quadrilateral finite element of four nodes with 32 DOFs. The present finite element (PE) is a combination of two finite elements. The first finite element is a linear isoparametric membrane element and the second is a high precision Hermitian element. One of the essential objectives of the current investigation is to confirm the capability and efficiency of the PE for stress determination in perforated laminates. Different geometric parameters, such as the cutout form, sizes and cutout orientations, which have a considerable effect on the stress values, are studied. Using the present finite element formulation, the obtained results are found to be in good agreement with the analytical findings, which validates the capability and the efficiency of the proposed formulation. Finally, to understand the material parameters effect such as the orientation of fibers and degree of orthotropy ratio on the stress values, many figures are presented using different ellipse major to minor axis ratio. The stress concentration values are considerably affected by increasing the orientation angle of the fibers and degree of orthotropy.
A simple four-node isoparametric finite element with five degrees of freedom, based on Reddy’s third-order shear deformation theory, is elaborated and used in a model for analizing the bending of ...laminated plates. The results obtained are compared with solutions given by the three-dimensional elasticity and other theories.
An axisymmetric problem of high strains in a spherical lead shell enclosed into an aluminum "spacesuit" under the influence of pulse overload is considered. The shell straining is described with the ...use of equations of mechanics of elastoviscoplastic media in Lagrangian variables. Kinematic relations are determined in the current state metrics. Equations of state are taken in the form of equations of the flow theory with isotropic hardening. Contact interaction of a shell and a "spacesuit" is modeled by conditions of non-penetration with friction. Numerical solution under the given boundary and initial conditions is based on the moment schema of the finite element method and the explicit time integration scheme of the "cross". For sampling the space variables 4-node isoparametric finite elements with multilinear forms features are used. As it was shown by the results of calculations, spherical shell suffers significant local forming, characterized by large displacements and rotation angles of finite elements as a rigid body in the process of loading. The calculation results of the residual form are in good agreement with the experimental data.
The method of computer simulation based on the application of isoparametric finite elements is used for the investigation of the distribution of mechanical stresses in a thin rigid plate connected ...with a thick-walled cylinder. We determine the maximum stresses in the concentrator (in the region of the plate–cylinder joint). For different materials, we construct the dependences of these stresses on the pneumatic (hydrostatic) pressure acting upon the plate, which are very important for practical purposes.
We study two fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation on an evolving surface, given a smooth potential with polynomial growth. In particular we establish ...optimal order error bounds for a (fully implicit) backward Euler time-discretisation, and an implicit-explicit time-discretisation, with isoparametric surface finite elements discretising space.
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