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CONTENTS
Volume 6, Number 6, September 1998
 

Abstract
A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and Levy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the Levy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.

Key Words
higher-order theory, Levy solutions, finite element solutions, Navier solutions, shear deformation, bending natural vibration

Address
Bose P, Texas A&M Univ, Dept Mech Engn, College Stn, TX 77843 USA
Texas A&M Univ, Dept Mech Engn, College Stn, TX 77843 USA

Abstract
A coupling system for a structure accelerating through a fluid is considered which is composed of the structure and the fluid in a finite surrounding volume. Based on the variational principle, the finite element equations of hydrodynamic pressure and structural elastic vibration are deduced. A numerical method is given for the dynamic character and response of the structure which takes the coupled fluid into account. The effect of axial inertial forces on the dynamic character and response of rapidly accelerating structures is also considered.

Key Words
structure/fluid interaction, dynamic response, added mass

Address
Liu ZX, Shanghai Jiao Tong Univ, Dept Engn Mech, Shanghai 200030, Peoples R China
Shanghai Jiao Tong Univ, Dept Engn Mech, Shanghai 200030, Peoples R China
Univ Cardiff, Cardiff Sch Engn, Div Struct Engn, Cardiff, S Glam, Wales

Abstract
Finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with various types of internal line supports. These plates are subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load. This is achieved by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of internal line support type and boundary conditions on the optimal ply angles and the buckling load are numerically studied. The laminate behavior with respect to fibre orientation changes significantly in the presence of internal line supports as compared to that of a laminate where there is no internal supporting. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without internal supporting differ substantially.

Key Words
optimal design, laminated plates, maximum buckling load, internal line supports, finite element method

Address
Walker M, Technikon Natal, CADENCE, Durban, South Africa
Technikon Natal, CADENCE, Durban, South Africa

Abstract
A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on an elastic foundation. The plate is assumed to be simply supported on its two opposite edges and the two side edges remain free. The initial geometrical imperfection of the plate is taken into account. The formulation are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates resting on Pasternak-type or softening nonlinear elastic foundations from which results for Winker elastic foundations follow as a limiting case. Typical results are presented in dimensionless graphical form.

Key Words
structural stability, thermal postbuckling, moderately thick plate, elastic foundation, Galerkin-perturbation method

Address
Shen HS, Shanghai Jiao Tong Univ, Dept Civil Engn, Shanghai 200030, Peoples R China
Shanghai Jiao Tong Univ, Dept Civil Engn, Shanghai 200030, Peoples R China

Abstract
Exercise of complete control on all aspects of any manufacturing / fabrication process is very difficult, leading to uncertainties in the material properties and geometric dimensions of structural components. This is especially true for laminated composites because of the large number of parameters associated with its fabrication. When the basic parameters like elastic modulus, density and Poisson\'s ratio are random, the derived response characteristics such as deflections, natural frequencies, buckling loads, stresses and strains are also random, being functions of the basic random system parameters. In this study the basic elastic properties of a composite lamina are assumed to be independent random variables. Perturbation formulation is used to model the random parameters assuming the dispersions small compared to the mean values. The system equations are analyzed to obtain the mean and the variance of the plate natural frequencies. Several application problems of free vibration analysis of composite plates, employing the proposed method are discussed. The analysis indicates that, at times it may be important to include the effect of randomness in material properties of composite laminates.

Key Words
composite laminates, material property randomness, perturbation method, natural frequencies, standard deviation of response

Address
Salim S, Indian Inst Technol, Dept Aerosp Engn, Kanpur 208016, Uttar Pradesh, India
Indian Inst Technol, Dept Aerosp Engn, Kanpur 208016, Uttar Pradesh, India

Abstract
In this paper, an analytic method to examine the random vibration of multispan Timoshenko frames due to a concentrated load traversing at a constant velocity is presented. A load\'s magnitude is a stationary process in time with a constant mean value and a variance. Two types of variances of this load are considered: white noise process and cosine process. The effects of both velocity and statistical characteristics of load and span number of the frame on both the mean value and variance of deflection and moment of the structure are investigated. Results obtained from a multispan Timoshenko frame are compared with those of a multispan Bernoulli-Euler frame.

Key Words
Timoshenko frames, random vibration, load, velocity, span number

Address
Wang RT, Natl Cheng Kung Univ, Dept Engn Sci, Tainan 70101, Taiwan
Natl Cheng Kung Univ, Dept Engn Sci, Tainan 70101, Taiwan

Abstract
This paper concerns studies on the shape formation of post-tensioned and shaped steel domes. The post-tensioned and shaped steel domes, assembled initially at ground level in an essentially flat condition, are shaped to a curved space form and erected into the final position by means of a posttensioning technique. Based on previous studies on this shape formation principle, three post-tensioned and shaped steel domes have been constructed. The results of the shape formation tests and finite element analyses are reported in this paper. It is found that the first two test domes did not furnish a part-spherical shape as predicted by finite element analyses, because the movements of some mechanisms were not controlled sufficiently. With a revised post-tensioning method, the third dome obtained the theoretical prediction. The test results of the three post-tensioned and shaped domes have shown that a necessary condition to form a desired space shape from a planar layout with low joint stiffnesses is that the movements of all the existing mechanisms must be effectively controlled as indicated by the finite element analysis. The extent of the maximum elastic deformation of a posttensioned and shaped steel structure is determined by the strength of the top chords and their joints. However, due to the semi-rigid characteristic of the top chord joints, the finite element analyses cannot give a close prediction for the maximum elastic deformations of the post-tensioned and shaped steel domes. The results of the current studies can be helpful for the design and construction of this type of structure.

Key Words
space structure, finite element, post-tensioning, construction

Address
Schmidt LC, Univ Wollongong, Dept Civil & Min Engn, Wollongong, NSW 2500, Australia
Univ Wollongong, Dept Civil & Min Engn, Wollongong, NSW 2500, Australia

Abstract
Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babuska-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges proposed by Hughes and Franca is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. Also, a solid mechanics problem is presented by which the stability of mixed elements can be studied. It is shown that the pressure solutions, although stable, are shown to exhibit sensitivity to the stabilization parameters.

Key Words
stabilization of pressure, pressure oscillations, pressure modes, incompressible materials, mixed finite elements, volumetric locking

Address
Lee SH, Yonsei Univ, Dept Civil Engn, Seoul 120749, South Korea
Yonsei Univ, Dept Civil Engn, Seoul 120749, South Korea

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