It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.

Crack tip finite elements are unnecessary

A review and catalogue of plate bending finite elements

In dynamic analyses using the finite element method very large matrices are derived. The size of the matrices is usually reduced using an eigenvalue economization method. This paper describes an automatic technique for selecting the optimum variables to be kept as masters using the economization method. Some examples are presented and these lead to an empirical statement about expected accuracy.

Automatic masters for eigenvalue economization

A general curved element of arbitrary shape for both thick and thin shells is proposed for the linear fracture analysis of a through crack in a shell or a plate. The element is derived from a degenerate 20-noded solid isoparametric element using reduced integration technique. The 1/√(r) singularity of the strains is obtained by the same procedure proposed earlier for two- and three-dimensional problems,1,2viz. by placing the mid-side nodes near the crack at the quarter points.



Several illustrated examples ranging from classical solutions to practical problems are given to assess the accuracy of solution attainable.

D. Walters

Papers

A new family of curvilinear plate bending elements for vibration and stability

On possible loss of accuracy in curved finite elements