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CONTENTS
Volume 10, Number 2, August 2000
 

Abstract
An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, Sigma(i)N(i)=1, some additional conditions to be satisfied by the shape functions of higher order elements are identified. Elements with their geometry in the natural form, i.e., without any geometrical distortion, satisfy most of these additional conditions inherently. However, the geometrically distorted elements satisfy only fewer conditions. The practical implications of the satisfaction or non-satisfaction of these additional conditions are investigated with respect to a 3-node bar element, and 8- and 9-node quadrilateral elements. The results suggest that non-satisfaction of these additional conditions results in poorer performance of the element when the element is geometrically distorted. Based on the new interpretation of completeness requirements, a 3-node element and an 8-node rectangular element that are insensitive to mid-node distortion under a quadratic displacement field have been developed.


Key Words
finite element, completeness requirements, distortion sensitivity, shape functions, geometric distortion, higher order elements

Address
Rajendran S, Nanyang Technol Univ, Sch Mech & Prod Engn, Ctr Adv Numer Engn Simulat, N3-B3C-10, Singapore 639798, Singapore
Nanyang Technol Univ, Sch Mech & Prod Engn, Ctr Adv Numer Engn Simulat, Singapore 639798, Singapore

Abstract
An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.

Key Words
reticulated spherical shells, characteristic geometrical parameter, stiffness of spring, snap-through buckling, asymptotic iteration method

Address
Nie GH, Tongji Univ, Dept Engn Mech, Key Lab Solid & Failure Mech MOE, Shanghai 200092, Peoples R China
Tongji Univ, Dept Engn Mech, Key Lab Solid & Failure Mech MOE, Shanghai 200092, Peoples R China

Abstract
The paper analyzes the problem of torsion in an adhesive non-tubular bonded single-lap joint. The joint considered consists of two thin rectangular section beams bonded together along a side surface. Assuming the materials involved to be governed by linear elastic laws, equilibrium and compatibility equations were used to arrive at an integro-differential relation whose solution makes it possible to determine torsional moment section by section in the bonded joint between the two beams. This is then used to determine the predominant stress and strain field at the beam-adhesive interface (stress field along the direction perpendicular to the interface plane, equivalent to the applied torsional moment and the corresponding strain field) and the joint\'s elastic strain (absolute and relative rotations of the bonded beam cross sections). All the relations presented were obtained in closed form. Results obtained theoretically are compared with those given by a three dimensional finite element numerical model. Theoretical and numerical analysis agree satisfactorily.

Key Words
non-tubular, single-lap, bonded joint, adhesive, torsion

Address
Pugno N, Politecn Torino, Dept Struct Engn, Turin, Italy
Politecn Torino, Dept Struct Engn, Turin, Italy
Politecn Turin, Dept Aeronaut & Space Engn, I-10129 Turin, Italy


Abstract
This paper concerns the development of a computational model for the damage evolution of engineering materials under dynamic loading. Two models describing the anisotropic damage evolution of a material are presented; the first is based on a power function of the effective equivalent stress and the second on the damage strain energy release rate. The methods for computing the damage accumulated in structural components and their implementation in a finite element programme are presented together with some numerical results. The dynamic response of a damaged structural component and the dynamic behaviour of a damaged material have been studied numerically. This study shows that the frequency spectrum of a damaged structure is down-shifted, while the damping ratio of damaged materials becomes higher, the amplitude of the response significantly increases and the resonance ensuing from the damage growth still occurs in a damaged structure.

Key Words
dynamic response, damage evolution law, damage-based FEM analysis

Address
Zhang WH, Zhejiang Univ, Inst Geotech Engn, Hangzhou 310027, Peoples R China
Zhejiang Univ, Inst Geotech Engn, Hangzhou 310027, Peoples R China

Abstract
This paper discusses the error propagation characteristics of the Newmark explicit method, modified Newmark explicit method and alpha-function dissipative explicit method in pseudodynamic tests. The Newmark explicit method is non-dissipative while the alpha-function dissipative explicit method and the modified Newmark explicit method are dissipative and can eliminate the spurious participation of high frequency responses. In addition, error propagation analysis shows that the modified Newmark explicit method and the alpha-function dissipative explicit method possess much better error propagation properties when compared to the Newmark explicit method. The major disadvantages of the modified Newmark explicit method are the positive lower stability limit and undesired numerical dissipation. Thus, the alpha-function dissipative explicit method might be the most appropriate explicit pseudodynamic algorithm.

Key Words
error propagation analysis, explicit pseudodynamic algorithm

Address
Chang SY, Natl Taiwan Univ, Natl Ctr Res Earthquake Engn, Taipei 10764, Taiwan
Natl Taiwan Univ, Natl Ctr Res Earthquake Engn, Taipei 10764, Taiwan

Abstract
An analytical model with tension softening for the prediction of the capacity of prestressed concrete beams under pure torsion and under torsion combined with shear and flexure is introduced. The proposed approach employs bilinear stress-strain relationship with post cracking tension softening branch for the concrete in tension and special failure criteria for biaxial stress states. Further for the solution of the governing equations a special numerical scheme is adopted which can be applied to elements with practically any cross-section since it utilizes a numerical mapping. The proposed method is mainly applied to plain prestressed concrete elements, but is also applicable to prestressed concrete beams with light transverse reinforcement. The aim of the present work is twofold; first, the validation of the approach by comparison between experimental results and analytical predictions and second, a parametrical study of the influence of concentric and eccentric prestressing on the torsional capacity of concrete elements and the interaction between torsion and shear for various levels of prestressing. The results of this investigation presented in the form of interaction curves, are compared to experimental results and code provisions.

Key Words
torsional strength, prestressed concrete, nonlinear analysis, torsion and shear, torsion with shear and flexure

Address
Karayannis CG, Democritus Univ Thrace, Dept Civil Engn, GR-67100 Xanthi, Greece
Democritus Univ Thrace, Dept Civil Engn, GR-67100 Xanthi, Greece

Abstract
A two-step procedure for the application of non linear constrained programming to the limit analysis of rigid brick-block systems with no-tension and frictional interface is implemented and applied to various masonry structures. In the first step, a linear problem of programming, obtained by applying the upper bound theorem of limit analysis to systems of blocks interacting through no-tension and dilatant interfaces, is solved. The solution of this linear program is then employed as initial guess for a non linear and non convex problem of programming, obtained applying both the \'mechanism\' and the \'equilibrium\' approaches to the same block system with no-tension and frictional interfaces. The optimiser used is based on the sequential quadratic programming. The gradients of the constraints required are provided directly in symbolic form. Ln this way the program easily converges to the optimal solution even for systems with many degrees of freedom. Various numerical analyses showed that the procedure allows a reliable investigation of the ultimate behaviour of jointed structures, such as stone masonry structures, under statical load conditions.

Key Words
limit analysis, mathematical programming, masonry

Address
C Baggio: Univ Roma Tre, Dipartimento Progettaz & Sci Architettura, I-4000184 Rome, Italy
P Trovalusci: Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma \"La Sapienza\", Via A. Gramsci, 53-00197 Roma, Italy


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