A C1 Bending Element for Composite Plates Based on a High-Order Shear Deformation Theory (original) (raw)
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Finite Elements in Analysis and Design, 2003
A triangular element based on Reddy's higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in ÿnite-element analysis. This is due to the di culties associated with satisfaction of inter-elemental continuity requirement of the plate theory. Keeping this aspect in view, the proposed element is developed where Reddy's plate theory is successfully implemented. It has six nodes and each node contains equal degrees of freedom. The performance of the element is tested with di erent numerical examples, which show its precision and range of applicability.
A rectangular non-conforming element based on Reddy's higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy's plate theory is successfully implemented. It has four nodes and each node contains 7 degrees of freedom. The performance of the element is tested with different numerical examples, which show its precision and range of applicability.
A refined higher-order C° plate bending element
Computers & Structures, 1982
A general finite element formulation for plate bending problem based on a higher-order displacement model and a threedimensional state of stress and strain is attempted. The theory incorporates linear and quadratic variations of transverse normal strain and transverse shearing strains and stresses respectively through the thickness of the plate. The 9-noded quadrilateral from the family of two dimensional Co continuous isoparametric elements is then introduced and its performance is evaluated for a wide range of plates under uniformly distributed load and with different support conditions and ranging from very thick to extremely thin situations. The effect of full. reduced and selective integration schemes on the final numerical result is examined. The behaviour of this element with the present formulation is seen to be excellent under all the three integration schemes.
World Journal of Mechanics, 2013
A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains (xz γ and yz γ) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.
A new developed shear deformation plate
This paper presents an improved higher-order shear deformation theory of plates. The theory is developed from the transverse shear deformation theory presented by Ambartsumian [1]. The present plate theory contains kinematics of higher-order displacement field of plates, a system of higher-order differential equilibrium equations in terms of the three generalized displacements of bending plates, and a system of boundary conditions at each edge of plate boundaries. The present shear deformation theory of plates is validated by applying it to solve torsional plates and simply supported plates. The obtained solutions using the present theory are compared with the solutions of other shear-deformation theories. A good agreement is achieved through these comparisons and the advantages of the present theory are clearly verified. The shear deformation plate theory presented here can be applied to the analysis of laminated composite plates to better predict their dynamic and static behaviors...
A refined higher-order generally orthotropic C0 plate bending element
Computers & Structures, 1988
finite element formulation for flexure of a generally orthotropic plate based on a higher-order displacement model and a three-dimensional state of stress and strain is presented here. This higher-order theory incorporates linear variation of transverse normal strain/stress and parabolic variation of transverse shear strains through the thickness of the plate. The nine-noded quadrilateral from the family of two-dimensional Co continuous isoparametric Lagrangian elements is then developed as a generally orthotropic higher-order element. The performance of this element is evaluated on square plates with different support conditions and under uniformly distributed and central point loads. The numerical results of the present formulation are compared with thin plate, elasticity and Mindlin/Reissner solutions. The effect of degree of orthotropy on the maximum bending moment location is examined for different loading and boundary conditions. The effect of directional orthotropy on the location of the maximum values for the various stress-resultants is also studied.
A higher order shear deformable finite element for homogeneous plates
Engineering Structures, 2003
A C 0 finite element is introduced for the analysis of thick plates with transverse shear and normal strain and nonlinear in-plane displacement distribution with respect to the plate thickness. The warping theory proposed by Hassis [1] is used for the equations governing the plate deformation. The analytical solutions of the plate deformation theory were compared with other higher-order theories and found to be predicting the thick plate behavior reasonably well. Based on this higher order shear deformation theory, an eight-node finite element is introduced for thick plates, and a computer program is developed. The warping functions used in the formulations presented simpler equations than the other higher order homogeneous models. The proposed element incorporates bending-stretching coupling via the additional terms introduced in the displacement field. Some example problems are solved and the results are compared with the exact and other mathematical solutions available in the literature. For comparison, both stress and displacement results are investigated. The results of the proposed element are found to be in good agreement with the literature.
A new finite element based on the strain approach with transverse shear effect
This research work deals with the development of a new Triangular finite element for the linear analysis of plate bending with transverse shear effect. It is developed in perspective to building shell elements. The displacements field of the element has been developed by the use of the strain-based approach and it is based on the assumed independent functions for the various components of strain insofar as it is allowed by the compatibility equations. Its formulation uses also concepts related to the fourth fictitious node, the static condensation and analytic integration. It is based on the assumptions of tick plate " s theory (Reissner-Mindlin theory). The element possesses three essential external degrees of freedom at each of the four nodes and satisfies the exact representation of the rigid body modes of displacements. As a result of this approach, a new bending plate finite element (Pep43) which is competitive, robust and efficient.
International Journal for Numerical Methods in Engineering, 2012
SUMMARYThis paper presents a new C0 eight‐node quadrilateral finite element (FE) for geometrically linear elastic plates. This finite element aims at modeling both thin and thick plates without any pathologies of the classical plate finite elements (shear and Poisson or thickness locking, spurious modes, etc). A C1 FE was previously developed by the first author based on the kinematics proposed by Touratier. This new FE can be viewed as an evolution towards three directions: (1) use of only C0 FE approximations; (2) modeling of thick to thin structures; and (3) capability in multifield problems. The transverse normal stress is included allowing use of the three‐dimensional constitutive law. The element performances are evaluated on some standard plate tests, and comparisons are given with exact three‐dimensional solutions for plates under mechanical and thermal loads. Comparisons are made with other plate models using C1 and semi‐C1 FE approximations as well as with an eight node C0...
Journal of Science and Technology in Civil Engineering (STCE) - NUCE
In this paper the smoothed four-node element with in-plane rotations MISQ24 is combined with a C0-type higher-order shear deformation theory (C0-HSDT) to propose an improved linear quadrilateral plate element for static and free vibration analyses of laminated composite plates. This improvement results in two additional degrees of freedom at each node and require no shear correction factors while ensuring the high precision of numerical solutions. Composite plates with different lay-ups, boundary conditions and various geometries such as rectangular, skew and triangular plates are analyzed using the proposed element. The obtained numerical results are compared with those from previous studies in the literature to demonstrate the effectiveness, the reliability and the accuracy of the present element. Keywords: composite laminated plates; bending problems; free vibration; C0-HSDT; MISQ24.