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The elliptic curved beam finite element for static and dynamic analysis of arches

Litewka P.

Foundations of Civil and Environmental Engineering

2011

No. 14

73--109

In this paper the physical curved beam finite element of elliptic shape was derived. Unlike for the typically used beam elements the shape functions derived here are not of constant coefficients but rather depend on physical and geometrical parameters of the element. To avoid elliptic integrals in the derivation the basic functions for the ellipse were replaced with their expansions into polynomial series. Thus, the shape functions obtained are quasi-exact solutions of differential equations for the deformed shape of the curved beam. The quasi-exact stiffness matrix was also derived as well as the consistent mass matrix. The derivations were carried out using the symbolic algebra program Maple. The performance of the element featuring no locking was checked in several numerical examples.

A sub-parametric shear deformable element for free vibration analysis of thick/thin rectangular plates with tapered thickness

Manna M. C.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 4

901-913

A sub-parametric shear deformable element is proposed for free vibration analysis of isotropic plates with linearly varying thickness in one direction. The element has sixteen nodes and thirty-six degrees of freedom. The transverse displacement and bending rotations are taken as independent field variables. The polynomials used to express these variables are of the same order. The geometry of the element is defined by a polynomial of lower order than the polynomials used for field variables. The entire formulation is made based on first-order shear deformation theory (FSDT). The rotary inertia is included in the consistent mass matrix for the analysis. Isotropic plates with different thickness ratios (varying from 0.01 to 0.2), tapered ratios, aspect ratios and boundary conditions are analyzed. The results obtained by the present element show an excellent agreement with the available published results. Some numerical results have been given as new results.