In-plane bending of Timoshenko beams in bilateral frictionless contact with an elastic half-space using a coupled FE-BIE method (original) (raw)

A mixed finite element formulation for timoshenko beam on winkler foundation

Computational Mechanics, 2003

A mixed formulation for Timoshenko beam element on Winkler foundation has been derived by defining the total curvature in terms of the bending moment and its second order derivation. Displacement and moment have been chosen as primary variables, while slope and first derivation of moment have been chosen as secondary variables. The behaviour matrix for Timoshenko beam element has been obtained in mixed form by using weak formulation with equilibrium and compatibility equations. The presented formulation makes the analysis of beams free of shear locking.

DQEM for free vibration analysis of Timoshenko beams on elastic foundations

Computational Mechanics, 2003

A differential quadrature element method (DQEM) based on first order shear deformation theory is developed for free vibration analysis of non-uniform beams on elastic foundations. By decomposing the system into a series of sub-domains or elements, any discontinuity in loading, geometry, material properties, and even elastic foundations can be considered conveniently. Using this method, the vibration analysis of general beam-like structures is to be studied. The governing equations of each element, natural compatibility conditions at the interface of two adjacent elements and the external boundary conditions are developed in a systematic manner, using Hamilton's principle. The present DQEM is to be implemented to Timoshenko beams resting on partially supported elastic foundations with various types of boundary conditions under the action of axial loading. The general versality, accuracy, and efficiency of the presented DQEM are demonstrated having solved different examples and compared to the exact or other numerical procedure solutions.

Free vibration of prestress Timoshenko beams resting on elastic foundation

Vietnam Journal of Mechanics, 2007

This paper presents a finite element formulation for investigating the free vibration of uniform Timoshenko beams resting on a Winkler-type elastic foundation and prestressing by axial force. Taking the effect of prestress, foundation support and shear deformation into account, a stiffness matrix for Timoshenko-type beam element is formulated using the energy method. The element consistent mass matrix is obtained from the kinetic energy using simple linear shape functions. Employing the formulated element, the natural frequencies of the beams having various boundary conditions are determined for different values of the axial force and foundation stiffness. The vibration Characteristics of the beams partially supported on the foundation are also studied and highlighted. Specially, the effects of shear deformation on the vibration frequencies of prestress beams fully and partially supported on the elastic foundation are investigated in detail.