Abstract
Green\'s functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed In terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green\'s functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.
Key Words
bi-materials, closed-form solutions, elasticity, Green\'s functions, integral transforms, point body forces, ring body forces, slipping interface, transversely isotropic solids
Address
Yue ZQ, NATL RES COUNCIL CANADA,INFRASTRUCT LAB,INST RES CONSTRUCT,OTTAWA,ON K1A 0R6,CANADA
Abstract
This paper describes a numerical and experimental study on the stability and failure behaviour of rectangular symmetric laminated composite plates. The plates are simply supported along the unloaded edges and clamped along the loaded ends, and they are subjected to uniaxial in-plane compression. The finite element method was employed for the theoretical study. The study examines the effect of the plate\'s stacking sequence and aspect ratio on the stability and failure response of rectangular symmetric laminated carbon fibre reinforced plastics composite plates. The study also includes the effect of the unloaded edge support conditions on the postbuckling response and failure of the plates, Extensive experimental investigation were also carried out to supplement the finite element study. A comprehensive comparison between theory and experimental data are presented and discussed in this contribution.
Key Words
stability, laminated composites, postbuckling, failure, flat panels
Abstract
The equivalent static force procedure and the response spectrum analysis method are widely used for seismic analyses of multi-story buildings. The equivalent static force procedure is one of the most simple but less accurate method in predicting possible seismic response of a structure. The response spectrum analysis method provides more accurate results while it takes much longer computational time.
In the response spectrum method, dynamic response of a multi-story building is obtained by combining modal responses through a proper procedure such as SRSS or CQC method. Since all of the analysis results are expressed in absolute values, structural engineers have difficulties to combine them with the results obtained from the static analysis. Design automation is interrupted at this stage because of the difficulty in the decision of the most critical design load.
Pseudo-dynamic analysis method proposed in this study provides more accurate seismic analysis results than those of the equivalent static force procedure since the dynamic characteristics of a structure is consider-ed. And the proposed method has an advantage in combination of the analysis results due to gravity loads and seismic loads since the direction of the forces can be considered.
Key Words
seismic analysis, equivalent static force procedure, response spectrum analysis method, pseudo-dynamic analysis method, lateral seismic force, story shear force, multi-story building
Address
Lee DG, SUNG KYUN KWAN UNIV,DEPT ARCHITECTURAL ENGN,SUWON 440746,SOUTH KOREA KYUNG HEE UNIV,DEPT ARCHITECTURAL ENGN,KYUNGKIDO 449701,SOUTH KOREA
Abstract
In this paper, both an approximate expression and an exact expression for the contribution factor of an element to the natural frequency of the finite element discretized system of a structure in general and a membrane in particular have been derived from the energy conservation principle and the finite element formulation of structural eigenvalue problems. The approximate expression for the contribution factor of an element is used to predict and determine the elements to be removed in an iteration since it depends only on the quantities associated with the old system in the iteration. The exact expression for the contribution factor of an element makes it possible to check whether the element is correctly removed at the end of an iteration because it depends on both the old system and the new system in the iteration. Thus, the combined use of the approximate expression and the exact expression allows a considerable number of elements to be removed in a single iteration so that the efficiency of the evolutionary structural optimization method can be greatly improved for solving the natural frequency optimization problem of a structure. A square membrane with different boundary supports has been chosen to investigate the general evolutionary path for the fundamental natural frequency of the structure. The related results indicated that if the objective of a structural optimization is to raise the fundamental natural frequency of the structure to an optimal value, the general evolutionary path during its optimization is that the elements are gradually removed along the direction from the area surrounded by the contour of the highest value to that surrounded by the contour of the lowest value.
Key Words
evolutionary criterion, natural frequency optimization, membrane vibration, general evolutionary path
Address
UNIV SYDNEY,FINITE ELEMENT ANAL RES CTR,FAC ENGN,SYDNEY,NSW 2006,AUSTRALIA VICTORIA UNIV TECHNOL,DEPT CIVIL & BLDG ENGN,MELBOURNE,VIC 3000,AUSTRALIA
Abstract
The dynamic buckling mechanism of a single-degree-of-freedom dissipative/nondissipative gradient system is thoroughly studied, employing energy criteria. The model is chosen in such a manner, that its corresponding static response is associated with all types of distinct critical points, Under a suddenly applied load of infinite duration it is found that dynamic buckling, occuring always through a saddle, leads to an escaped motion, which is finally attracted by remote stable equilibrium positions, belonging sometimes also to complementary paths. Moreover, although the existence of initial imperfection changes the static behaviour of the system from limit point instability to bifurcation, it is established that the proposed model is dynamically stable in the large, regardless of the values of all other parameters involved.
Key Words
critical points, dynamic buckling, saddle, stable in the large, snapping
Abstract
This paper is concerned with the structural optimization problem of maximizing the compressive buckling load of orthotropic rectangular plates for a given volume of material. The optimality condition is first derived via variational calculus. It states that the thickness distribution is proportional to the strain energy density contrary to popular claims of constant strain energy density at the optimum. An engineers physical meaning of the optimality condition would be to make the average strain energy density with respect to the depth a constant. A double cosine thickness varying plate and a double sine thickness varying plate are then fine tuned in a one parameter optimization using the Rayleigh-Ritz method of analysis. Results for simply supported square plates indicate an increase of 89% in capacity for an orthotropic plate having 100% of its fibers in 0 degrees direction.
Abstract
Finite element stiffness matrix methods are presented for finding natural frequencies (or buckling loads) and modes of repetitive structures. The usual approximate finite element formulations are included, but more relevantly they also permit the use of \'exact finite elements\', which account for distributed mass exactly by solving appropriate differential equations, A transcendental eigenvalue problem results, for which all the natural frequencies are found with certainty. The calculations are performed for a single repeating portion of a rotationally or linearly (in one, two or three directions) repetitive structure. The emphasis is on rotational periodicity, for which principal advantages include: any repeating portions can be connected together, not just adjacent ones; nodes can lie on, and members along, the axis of rotational periodicity; complex arithmetic is used for brevity of presentation and speed of computation; two types of rotationally periodic substructures can be used in a multi-level manner; multi-level non-periodic substructuring is permitted within the repeating portions of parent rotationally periodic structures or substructures and; all the substructuring is exact, i.e., the same answers are obtained whether or not substructuring is used. Numerical results are given for a rotationally periodic structure by using exact finite elements and two levels of rotationally periodic substructures. The solution time is about 500 times faster than if none of the rotational periodicity had been used. The solution time would have been about ten times faster still if the software used had included all the substructuring features presented.
Key Words
vibration, natural frequencies, space frames, periodic structures, multi-level substructuring
Address
Williams FW, UNIV WALES COLL CARDIFF,SCH ENGN,DIV STRUCT ENGN,CARDIFF CF2 1XH,S GLAM,WALES
Abstract
A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic X-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious-zero energy modes and Poisson\'s ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.
Key Words
8-node solid element, hierarchical mid-edge displacement, rotational degrees of freedom, corner rotations, mixed variational principles, non-conforming modes
Address
Choi CK, KOREA ADV INST SCI & TECHNOL,DEPT CIVIL ENGN,TAEJON 305701,SOUTH KOREA KOREA POWER ENGN CO INC,YONGIN 449910,SOUTH KOREA