Dynamics of transversely vibrating beams using four engineering theories

1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

Stress projection for membrane and shear locking in shell finite elements

A higher order beam finite element for bending and vibration problems

On locking-free shear deformable beam finite elements

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.

GR Bhashyam

Papers

Reduced integration and the shear-flexible beam element

Galerkin finite element method for non-linear beam vibrations

The second frequency spectrum of Timoshenko beams