Ray W. Clough

Finite element applications in the characterization of elastic solids

Abstract A finite element formulation of the minimum potential energy theorem is used to establish the basis for an experimental test program in composite and non-composite materials. The flexibility of the variational technique permits the experimental program to incorporate specimens of arbitrary geometry with a wide variety of stress and kinematic boundary conditions. The resulting experimental program utilizes comparisons between mathematical results and experimental measurements to evaluate the analytical accuracy of resulting approximate mechanical descriptions.

A finite element approximation for the analysis of thin shells

Abstract An approximate numerical analysis procedure is presented which is capable of solving thin shells of arbitrary shape, boundary conditions and loading. The shell is idealized as an assemblage of triangular finite elements representing both membrane and flexural stiffness properties, and the solution is carried out by digital computer. Five examples are presented which demonstrate the versatility of the procedure in treating different shell configurations, as well as the accuracy of the results which may be obtained.

Dynamic analysis of large structural systems with local nonlinearities

Abstract In many types of structures that exhibit significant nonlinearity during dynamic response the nonlinear stiffness property is confined to a few predetermined localities. This physical characteristic may be exploited by making use of substructure concepts in the dynamic response analysis. The elastic components may be represented by a small matrix of stiffness coefficients coupling them to the nonlinear elements, and only the properties of the few nonlinear elements need be modified during the response analysis. Both direct and indirect techniques for taking advantage of localized nonlinearity are reviewed here. In the direct methods the equations of motion are integrated by step-by-step procedures. Various methods of reducing the effective number of degrees of freedom are discussed. In the indirect methods the response to simple loadings is determined, and the response to the prescribed loading is obtained by superposition. A technique for applying superposition to the linear portion of the structure while treating the nonlinear region by a step-by-step procedure is described.

Dynamic finite element analysis of arbitrary thin shells

Abstract A brief review of the development of finite element procedures for the analysis of thin shells is presented, together with a discussion of the four types of approximations involved in the application of the method. Then two factors which influence the efficiency of the finite element solution are considered: the properties of the individual elements (including curvature, deformation refinement, etc.) and the nodal degree of freedom representing rotation about the shell surface normal. Comparative analyses are presented to illustrate the influence of these factors in practical cases. Finally, the formulation of the finite element system equations of motion is discussed and techniques of solution are outlined, taking account of both linear and non-linear classes of problems. A series of examples (both linear and non-linear) are presented which demonstrate the effectiveness and generality of this dynamic analysis technique.

The finite element method after twenty-five years: A personal view

Abstract The purpose of this paper is to examine the current state of development of the finite element method with regard to engineering applications. First is presented a personal view of the origins of the method, describing the sequence of events at Berkeley. Next is a discussion of the state-of-the-art of structural dynamic analysis, with mention of important recent advances. Finally, two examples drawn from earthquake engineering experience are discussed which demonstrate some limitations of present capabilities. Specific areas requiring new program development are mentioned; the need for a combined analytical-experimental approach is emphasized.

Original formulation of the finite element method

Following a brief summary of the 1952 state of the art of structural analysis, the paper describes the circumstances that led to the formulation of the finite element method by members of the Structural Dyanmics Unit at the Boeing Airplane Company. It is noted that the central feature of the procedure that was developed is the evaluation of the stiffness properties of structural elements based on assumed sets of displacement interpolation functions.

AREAS OF APPLICATION OF THE FINITE ELEMENT METHOD

Abstract The development of the finite element method, from its initial formulation as a generalized procedure for the analysis-of airplane structures to a completely general tool for the solution of problems of continuum mechanics, is outlined briefly. Its great advantage in providing the basis for development of general purpose structural analysis computer programs is emphasized, and then the generality of the procedure is demonstrated by presentation of a series of example analyses. The examples have been taken primarily from the practical engineering world and include problems associated with concrete and earth dams, with shell structures (including cooling towers, tubular joints for offshore structures, and nuclear reactors), as well as cases involving three-dimensional solids. The treatment of dynamic as well as static loadings is discussed, and the analysis of non-linear geometric and material behavior is mentioned. Also, reference is made to the application of the finite element method to other types of field problems such as heat conduction and seepage through porous media. The paper is purely descriptive and includes no mathematical derivations or formulae.

Recent concrete dams engineering in China

This is a discussion of personal experiences related to the engineering of concrete dams in China. Included in the discussion are considerations of the behavior of dams during earthquakes.