A simple correction to the first-order shear deformation shell finite element formulations

2000 ◽  
Vol 35 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Romil Tanov ◽  
Ala Tabiei
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
First Order ◽  
Shell Finite Element ◽  
Finite Element Formulations

scholarly journals A COMBINED STRAIN ELEMENT TO FUNCTIONALLY GRADED STRUCTURES IN THERMAL ENVIRONMENT

2020 ◽  
Vol 60 (6) ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Element Analysis ◽  
First Order ◽  
Graded Structures

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.

Geometrically nonlinear finite element simulation of smart laminated shells using a modified first-order shear deformation theory

2019 ◽  
Vol 30 (4) ◽  
pp. 517-535 ◽  
Author(s):  
Hanen Mallek ◽  
Hanen Jrad ◽  
Mondher Wali ◽  
Fakhreddine Dammak
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Piezoelectric Materials ◽  
Shear Deformation Theory ◽  
Nonlinear Finite Element ◽  
Shear Stresses ◽  
Geometrically Nonlinear ◽  
Element Analysis ◽  
First Order

This article investigates geometrically nonlinear and linear analysis of multilayered shells with integrated piezoelectric materials. An efficient nonlinear shell element is developed to solve piezoelastic response of laminated structure with embedded piezoelectric actuators and sensors. A modified first-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The electric potential is assumed to be a linear function through the thickness of each active sub-layer. Several numerical tests for different piezolaminated geometries are conducted to highlight the reliability and efficiency of the proposed implementation in linear and geometrically nonlinear finite element analysis.

p-Version Axisymmetric Shell Element for Geometrically Nonlinear Analysis

1992 ◽  
Author(s):  
Joseph H. Liu ◽  
Karan S. Surana
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Shell Element ◽  
Element Approximation ◽  
Geometrically Nonlinear ◽  
Present Formulation ◽  
Geometrically Nonlinear Analysis ◽  
Axisymmetric Shell ◽  
Shell Finite Element ◽  
Finite Element Formulations

Abstract This paper presents a p-version geometrically nonlinear (GNL) formulation based on total Lagrangian approach for a three node curved axisymmetric shell element. The approximation functions and the nodal variables for the element are derived directly from the Lagrange family of interpolation functions of order pξ and pη. This is accomplished by first establishing one dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three and one node equivalent configurations that correspond to pξ + 1 and pη + 1 equally spaced nodes in the ξ and η directions and then taking their products. The resulting element approximation functions and the nodal variables are hierarchical and the element approximation ensures C0 continuity. The element geometry is described by the coordinates of the nodes located on the middle surface of the element and the nodal vectors describing top and bottom surfaces of the element. The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete axisymmetric state of stresses and strains are considered hence the element is equally effective for very thin as well as extremely thick shells. The formulation presented here removes virtually all of the drawbacks present in the existing GNL axisymmetric shell finite element formulations and has many additional benefits. First, the currently available GNL axisymmetric shell finite element formulations are based on fixed interpolation order and thus are not hierarchical and have no mechanism for p-level change. Secondly, the element displacement approximations in the existing formulations are either based on linearized (with respect to nodal rotation) displacement field in which case a true Lagrangian formulation is not possible and the load step size is severely limited or are based on nonlinear nodal rotation functions approach in which case though the kinematics of deformation is exact but additional complications arise due to the noncummutative nature of nonlinear nodal rotation functions. Such limitations and difficulties do not exist in the present formulation. The hierarchical displacement approximation used here does not involve traditional nodal rotations that have been used in the existing shell element formulations, thus the difficulties associated with their use are not present in this formulation. Incremental equations of equilibrium are derived and solved using the standard Newton-Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a present tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the literature.

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