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CONTENTS
Volume 3, Number 2, March 1995
 

Abstract
A soil-structure interaction formulation is used here which is based on consideration of the dynamics of the structure with a free, rather than a fixed, base. This approach is shown to give a quite simple procedure for coupling the dynamic characteristics of the structure to those of the foundation and soil in order to obtain a matrix formulation for the complete system. In fixed-base studies it is common to presume that each natural mode of the structure has a given fraction of critical damping, and since the interaction formulation uses a free-base model, it seems natural for this situation to assign the equal modal damping values to free-base modes. It is shown, though, that this gives a structural model which is significantly different than the one having equal modal damping in the fixed-base modes. In particular, it is found that the damping matrix resulting in equal modal damping values for free-based modes will give a very significantly smaller damping value for the fundamental distortional mode of the feued-base structure. Ignoring this fact could lead one to attribute dynamic effects to interaction which are actually due to the choice of damping.

Key Words
DAMPING, MODAL ANALYSIS, MODELING, SEISMIC ANALYSIS, SOIL-STRUCTURE INTERACTION, VIBRATION

Address
LUTES LD, TEXAS A&M UNIV,DEPT CIVIL ENGN,COLLEGE STN,TX 77843
GEORGE WASHINGTON UNIV,DEPT CIVIL ENGN,WASHINGTON,DC 20052

Abstract
It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories, These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.


Key Words
3RD-ORDER THEORIES, ELASTICITY, FLEXURE, COMPOSITE, LAMINATED, LAYER INTERFACE, CONTINUITY, DEGREES OF FREEDOM, ANALYTICAL, FINITE ELEMENT METHOD, SYMMETRICAL LAY-UP, ANTISYMMETRIC LAY-UP, CROSS-PLY, ANGLE-PLY

Address
SINGH G, VIKRAM SARABHAI SPACE CTR,STRUCT ENGN GRP,DIV STRUCT DESIGN & ANAL,TRIVANDRUM 695022,KERALA,INDIA
INDIAN INST TECHNOL,DEPT AEROSP ENGN,KANPUR 208016,UTTAR PRADESH,INDIA

Abstract
Since structural systems may fail in any one of several failure modes, computation of system reliability is always difficult. A method using numerical quadrature for computing structural system reliability with either one or more than one failure mode is presented in this paper. Statistically correlated safety margin equations are transformed into a group of uncorrelated variables and the joint density function of these uncorrelated variables can be generated by using the Maximum Entropy Method. Structural system reliability is then obtained by integrating the joint density function with the transformed safety domain enclosed within a set of linear equations. The Gaussian numerical integration method is introduced in order to improve computational accuracy. This method can be used to evaluate structural system reliability for Gaussian or non-Gaussian variables with either linear or nonlinear safety boundaries. It is also valid for implicit safety margins such as computer programs. Both the theory and the examples show that this method is simple in concept and easy to implement.

Key Words
STRUCTURAL SYSTEM RELIABILITY, NUMERICAL INTEGRATION, MAXIMUM ENTROPY METHOD, COMPUTATIONAL ACCURACY

Address
ZHU TL, NORTHWESTERN POLYTECH UNIV,DEPT AIRCRAFT ENGN,XIAN 710072,PEOPLES R CHINA

Abstract
A damped trapezoidal rule method for numerical time-integration is presented, and its application in analyses of dynamic response of damped structures is discussed. It is shown that the damped trapezoidal rule method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are developed for the damped single-degree-of-freedom systems. Error analyses are also performed for the Newmark beta method and compared with the damped trapezoidal rule method as a basis for discussion of the relative merits of the proposed method. The procedure is fully explicit and easy to implement. However, since the method is an explicit method, it is conditionally stable. The methodology is applied to several example problems to illustrate its strengths, limitations and inherent simplicity.

Key Words
NUMERICAL TIME-INTEGRATION, STRUCTURAL DYNAMICS, STABILITY ANALYSIS, EXPLICIT METHOD, IMPLICIT METHODS, ERROR ANALYSIS, TRAPEZOIDAL RULE METHOD

Address
PEZESHK S, MEMPHIS STATE UNIV,DEPT CIVIL ENGN,MEMPHIS,TN 38152

Abstract
A simple numerical method is applied to calculate the large deflection of a cantilever beam under an elastic-plastic deformation by dividing the deformed axis into a number of small segments. Assuming that each segment can be approximated as a circular are, the method allows large deflections and plastic deformation to be analyzed. The main interests are the load-deflection relationship, curvature distribution along the beam and the length of the plastic region. The method is proved to be easy and particularly versatile. Comparisons with other studies are given.

Key Words
LARGE DEFLECTION, ELASTIC PLASTIC DEFORMATION, CANTILEVERS, CURVATURE

Address
WANG B, NANYANG TECHNOL UNIV,SCH MECH & PROD ENGN,SINGAPORE 2263,SINGAPORE
UNIV MANCHESTER,INST SCI & TECHNOL,DEPT MECH ENGN,MANCHESTER M60 1QD,LANCS,ENGLAND

Abstract
A new vector algorithm is presented for computing the stiffness matrices of layered reinforced concrete shell elements. Each element stiffness matrix is represented in terms of three vector arrays of lengths 78, 96 and 36, respectively. One element stiffness matrix is calculated at a time without interruption in the vector calculations for the uncracked or cracked elements. It is shown that the present algorithm is 1.1 to 7.3 times more efficient then a previous algorithm developed by us on a Gray Y-MP supercomputer.

Key Words
VECTOR ALGORITHM, ELEMENT STIFFNESS MATRIX, INELASTIC FINITE ELEMENT ANALYSIS, CRAY Y-MP, SUPERCOMPUTER

Address
MIN CS, CHEJU NATL UNIV,DEPT OCEAN CIVIL ENGN,CHEJU,SOUTH KOREA
N CAROLINA STATE UNIV,CTR NUCL POWER PLANT STRUCT EQUIPMENT & PIPING,RALEIGH,NC 27695

Abstract
A numerical algorithm for plane stress and shell elasto-plasticity is presented in this paper. The proposed strain decomposition (SD) algorithm is an elastic predictor/plastic corrector algorithm, and in the context of operator splitting, is a return mapping algorithm. However, it differs significantly from other return mapping algorithms in that only the necessary response functions are used without invoking their gradients, and the stress increment is updated only at the end of the time step. This makes the proposed SD algorithm more suitable for materials with complex yield surfaces and will guard against error accumulation during the time step. Comparative analyses of structural systems using the proposed strain decomposition (SD) algorithm and the iterative radial return (IRR) algorithm are presented. The results demonstrate the accuracy and usefulness of the proposed algorithm.

Key Words
ALGORITHM, FINITE ELEMENT, NUMERICAL TECHNIQUE, PLANE STRESS, PLASTICITY, SHELL

Address
LIU Z, UNIV QUEENSLAND,DEPT CIVIL ENGN,ST LUCIA,QLD 4072,AUSTRALIA

Abstract
Two kinds of special 3-dimensional 12-node finite elements-each one contains a traction-free planar surface-have been developed based on Hellinger-Reissner principle by assumed stress hybrid method. Example solutions have demonstrated the advantage of using these special elements for analyzing plates and solids with rectangular holes.

Key Words
RECTANGULAR HOLE, SPECIAL HYBRID STRESS ELEMENT

Address
TIAN ZS, UNIV SCI & TECHNOL CHINA,GRAD SCH,DEPT MECH,BEIJING 100080,PEOPLES R CHINA


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