Journal ArticleDOI
Reduced integration and the shear-flexible beam element
Gangan Prathap,GR Bhashyam +1 more
TLDR
In this paper, a penalty type argument is used to degenerate thick elements to thin elements, and various approximations of the shear related energy terms act as different types of constraints.Abstract:
The Timoshenko beam element is studied in an investigation of shear locking in the development of C(0) continuous elements using shear-flexible or penalty function type formulations. A penalty type argument is used to degenerate thick elements to thin elements, and the various approximations of the shear related energy terms act as different types of constraints. Depending on the formulation, two types of constraints may emerge, which are classified as true or spurious. Formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation. The argument is extended to a shallow curved Timoshenko beam, and another mechanism, inplane locking, arises if all energy terms corresponding to the membrane energy are exactly integrated.read more
Citations
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Journal ArticleDOI
Stress projection for membrane and shear locking in shell finite elements
Journal ArticleDOI
A higher order beam finite element for bending and vibration problems
Paul R. Heyliger,J. N. Reddy +1 more
TL;DR: In this paper, the finite element equations for a variationally consistent higher-order beam theory are presented for the static and dynamic behavior of rectangular beams, which correctly accounts for the stress-free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution.
Journal ArticleDOI
On locking-free shear deformable beam finite elements
TL;DR: In this article, a locking-free finite element model using the form of the exact solution of the Timoshenko beam theory is developed, which yields exact nodal values for the generalized displacements for constant material and geometric properties of beams.
Journal ArticleDOI
Shear and membrane locking in curved C0 elements
TL;DR: In this article, the locking phenomena in C 0 curved finite elements are studied for displacement, hybrid-stress and mixed formulations, and it is shown that for a curved beam element, locking is interrelated and either shear or membrane underintegration can alleviate it.
Journal ArticleDOI
Free vibration of composite beams using a refined shear flexible beam element
TL;DR: In this article, a finite element model based on a higher-order shear deformation theory is developed to study the free vibration characteristics of laminated composite beams and the effects of in-plane inertia and rotary inertia are considered in the formulation of the mass matrix.
References
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Journal ArticleDOI
Reduced integration technique in general analysis of plates and shells
TL;DR: In this article, a simple extension is made which allows the element to be economically used in all situations by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties.
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A simple and efficient finite element for plate bending
TL;DR: In this paper, a simple and efficient finite element is introduced for plate bending applications, where Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration, and the element is surprisingly accurate.
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Reduced and selective integration techniques in the finite element analysis of plates
TL;DR: In this paper, the authors developed a thin plate theory in which transverse shear strains are accounted for, and the variables in the theory are all kinematic, namely, displacements and independent rotations.
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A simple quadrilateral shell element
TL;DR: In this article, the authors describe a new four-noded quadrilateral shell element called QUAD4, which is based on isoparametric principles with modifications which relax excessive constraints.
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A study of quadrilateral plate bending elements with ‘reduced’ integration
TL;DR: In this paper, a series of numerical experiments on five different quadrilateral thick plate elements demonstrates the use of reduced integration and indicates the main reason for its success, which is the relaxation of a constraint on the shear strains.