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CONTENTS
Volume 4, Number 1, January 1996
 

Abstract
A new error measure for a static finite element analysis is proposed. This error measure is a modification to the Zienkiewicz and Zhu energy norm. The new error estimator is a global error measure for the analysis and is independent of finite element model size and internal stresses, hence it is readily transportable to other error calculations. It is shown in this paper the the new error estimator also produces conservative error measurements, making it a suitable procedure to adopt in commerical packages.

Key Words
finite elements, static analysis, error estimation

Address
Stephen DB, UNIV SYDNEY,DEPT AERONAUT ENGN,SYDNEY,NSW 2006,AUSTRALIA

Abstract
The behaviour of elasto-plastic planar arches subjected to dynamic loads in presented. The governing equations are formulated through the dynamic equations and compatibility conditions. The latter is established by applying the generalized conjugate segment analogy. Bending moments at the nodes and axial forces in the members are considered as primary variables in the elastic regime. They are supplemented by the rotations at the nodes and dislocations in the elements when plastic hinges occur. Newmark-beta method is adopted in the time marching process. The interaction diagram of each element is treated as the yield surface for the element and the associated flow rule is enforced as plastic flow occurs. The method provides good prediction of dynamic response of elasto-plastic arches while requiring small core storage and short computer time.

Key Words
arches, dynamic response, elasto-plastic, plastic hinge, yield surface

Address
Lee SL, NATL UNIV SINGAPORE,DEPT CIVIL ENGN,10 KENT RIDGE CRESCENT,SINGAPORE 0511,SINGAPORE

Abstract
This paper describes a continuum variational formulation for design optimization of nonlinear structures in the elastic-plastic domain, where unloading and reloading of the structures are allowed to occur. The Total Lagrangian procedure is used for the description of the structural deformation. The direct differentiation approach is used to derive the sensitivities of the various structural response measures with respect to the design parameters. Since the material goes into the inelastic range and unloading and reloading of the structure are allowed to occur, the structural response is path dependent and an additional step is needed to integrate the constitutive equations. It can be shown, consequently, that design sensitivity analysis is also path-dependent. The theory has been discretized by the finite element technique and implemented in a structural analysis code. Mathematical programming approach is used for the optimization process. Numerical applications on trusses are performed, where cross-sectional areas and nodal point coordinates are treated as design variables. Optimal designs have been obtained and compared by using two different strategies: a two level strategy where the levels are defined accordingly the type of design variables, cross sectional areas or node coordinates, and optimizing simultaneously with respect to both types of design variables.

Key Words
optimal design, non-linear, structures

Address
Valido AJ, ESCOLA SUPER TECNOL,INST POLITECN SETUBAL RUA VALE CHAVES,P-2910 SETUBAL,PORTUGAL

Abstract
The paper considers the elastic distortional buckling of overhanging beams, which consist of an internal segment with a cantilevered segment continuous over an internal support. The beams were considered loaded by a concentrated load at the cantilever tip, and the beams were either partially restrained or laterally restrained over the internal support. An efficient line-type finite element developed previously by the author was modified to incorporate loading remote from the shear centre, as well as to allow for lateral buckling without distortion. Buckling loads were obtained for a range of geometry when the load was placed on the top flange, at the shear centre or on the bottom flange. Buckling mode shapes were also obtained, and conclusions drawn regarding the influence of distortion on the overall buckling load.

Key Words
buckling, distortion, elasticity, modes, overhanging beams

Address
Bradford MA, UNIV NEW S WALES,SCH CIVIL ENGN,DEPT STRUCT ENGN,SYDNEY,NSW 2052,AUSTRALIA

Abstract
This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. ?his highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum are-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

Key Words
bar, beam, elastica, elliptic-integrals, shooting-optimization, large deflections, variable-arc-length beam

Address
Chucheepsakul S, KING MONGKUTS INST TECHNOL THONBURI,DEPT CIVIL ENGN,BANGKOK 10140,THAILAND
NATL UNIV SINGAPORE,DEPT CIVIL ENGN,SINGAPORE 0511,SINGAPORE

Abstract
The time-stepping boundary element method has been so far applied by the authors to transient heat conduction in isotropic solids as well as in orthotropic solids. In this paper. attempt is made to extend the method to 2-D transient heat conduction in arbitrarily anisotropic solids. The resulting boundary integral equation is discretized by means of the boundary element with quadratic interpolation. The final system of equations thus obtained is solved by advancing the time step from the given initial state to the final state. Through numerical compuation of a few examples the potential usefulness of the proposed method is demonstrated.


Key Words
boundary element method, integral equation formulation, numerical analysis, time-stepping approximation, time-dependent problem, heat conduction, anisotropic solid

Address
Tanaka M, SHINSHU UNIV,FAC ENGN,DEPT MECH ENGN,500 WAKASATO,NAGANO 380,JAPAN
SHINSHU UNIV,GRAD SCH,NAGANO,JAPAN

Abstract
In Lagrangian mechanics, attention is directed at the body as it moves through space. The region occupied by the body is called a configuration. All body points are labelled by the position they would have if the body were to occupy a chosen reference configuration. The reference configuration can be regarded as an extra fictional copy where notes are kept.

As the body moves and deforms, it is important to correctly observe the use of each configuration for computational purposes. The description of strain is particularly important. The present work establishes clearly the role of each configuration in total and in incremental forms. This work also details the differences between gradient and configurational calculus


Key Words
large displacement, strain Lagrangian, configurational calculus, gradient, equilibrium principle

Address
Underhill WRC, MCMASTER UNIV,DEPT MECH ENGN,HAMILTON,ON L8S 4L7,CANADA
MCMASTER UNIV,DEPT CIVIL ENGN & ENGN MECH,HAMILTON,ON L8S 4L7,CANADA

Abstract
In Lagrangian mechanics, attention is directed at the body as it moves through space. Each body point is identified by the position it would have if the body were to occupy an arbitrary reference configuration. A result of this approach is that the analyst often describes the body by using quantities that may involve more than one configuration. This is particularly common in incremental calculations and in changes of the choice of reference configuration. With the rise of very powerful computing machinery, the popularity of numerical calculation has become great. Unfortunately, the mechanical theory has been evolved in a piecemeal fashion so that it has become a conglomeration of differently developed patches. The current work presents a unified development of the equilibrium principle. The starting point is the conservation of momentum. All details of configuration are shown. Finally, full dynamic and static forms are presented for total and incremental work.

Key Words
large displacement, equilibrium principle, updated Lagrangian

Address
Underhill WRC, MCMASTER UNIV,DEPT MECH ENGN,HAMILTON,ON L8S 4L7,CANADA
MCMASTER UNIV,DEPT CIVIL ENGN & ENGN MECH,HAMILTON,ON L8S 4L7,CANADA

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