Abstract
This paper deals with the formulation and solution of a wide class of-structures, in the presence of both geometric and material nonlinearities, as a particular mathematical programming problem. We first present key ideas for the nonholonomic (path dependent) rate formulation for a suitably discretized structural model before we develop its computationally advantageous stepwise holonomic (path independent) counterpart. A feature of the final mathematical programming problem, known as a nonlinear complementarity problem, is that the governing relations exhibit symmetry as a result of the introduction of so-called nonlinear. \'\'residuals\'\'. One advantage of this form is that it facilitates application of a particular iterative algorithm, in essence a predictor-corrector method, for the solution process. As an illustrative example, we specifically consider the simplest case of plane trusses and detail in particular the general methodology for establishing the static-kinematic relations in a dual format. Extension to other skeletal structures is conceptually transparent. Some numerical examples are presented to illustrate applicability of the procedure.
Key Words
elastoplastic analysis, large displacement, mathematical programming, nonlinear complementarity problem, structural plasticity
Address
TinLoi F, UNIV NEW S WALES,SCH CIVIL ENGN,SYDNEY,NSW 2052,AUSTRALIA
Abstract
The ultimate behavior of a reinforced concrete hyperbolic paraboloid saddle shell under uniformly distributed vertical load is investigated using an inelastic, large displacement finite-element program originally developed at North Carolina State University. Unlike with the author\'s previous study which shows that the saddle shell possesses a tremendous capacity to redistribute the stresses, introducing tension stiffening in the model the cracks developed are no longer through cracks and formed as primarily bending cracks. Even though with small tension stiffening effect, the behavior of the shell is changed markedly from the one without tension stiffening effect. The load-deflection curves are straight and the slope of the curves is quite steep and remains unchanged with varying the tension stiffening parameters. The failure of the shell took place quite suddenly in a cantilever mode initiated by a formation of yield lines in a direction parallel to the support-to-support diagonal. The higher the tension stiffening parameters the higher is the ultimate load. The present study shows that the ultimate behavior of the shell primarily depends on the concrete tensile characteristics, such as tensile strength (before cracking) and the effective tension stiffening (after cracking). As the concrete characteristics would vary over the life of the shell, a degree of uncertainty is involved in deciding a specified ultimate strength of the saddle shell studied. By the present study, however, the overload factors based on ACI 318-95 are larger than unity for all the cases studied except that the tension stiffening parameter is weak by 3 with and without the large displacement effect, which shows that the Lin-Scordelis saddle shell studied here is at least safe.
Key Words
reinforced concrete shells, hyperbolic paraboloid saddle shell, nonlinear finite element
Address
Min CS, CHEJU NATL UNIV,CHEJU 690756,SOUTH KOREA
Abstract
Stiffness and flexibility equations are combined in the buckling analysis of a braced structure - stiffness for the original structure and flexibility for the bracing. Choosing a flexibility formulation for the bracing gives a very compact computational problem. It also gives theoretical insights into the behaviour of the braced structure.
Key Words
buckling, eigenvalues & eigenvecters, bracing, stiffness, flexibility
Address
Barbato J, UNIV NEW S WALES,SCH CIVIL ENGN,SYDNEY,NSW 2052,AUSTRALIA
Abstract
This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fu;ed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.
Key Words
elliptic-integrals, large deflections, variable-arc-length bars, beams, elasticas
Abstract
In this paper the ultimate strength of the R/C cooling towers, which have initial imperfection and pre-cracked elements, is analyzed. The initial geometric imperfections arise from the unavoidable inaccuracies under the construction and the pre-cracks are assumed to be produced by the temperature stress gradients or cyclic loading under wind pressure and/or earthquake load. Both effects are strongly influenced on the strength of the R/C cooling tower shell structures. The reinforcing ratio is also the important factor to evaluate the ultimate strength of the R/C cooling tower shells. However we could not analyze these structures experimentally because of their large, analyses are the powerful schemes to evaluate the safety and reliability of these structures. The analyzed model is Port Gibson cooling tower shell. In the numerical analysis the geometric and material nonlinearities are taken into account.
Key Words
R/C shell, finite element analysis, ultimate strength, geometric imperfection, cooling tower
Abstract
A procedure is being developed for bolting plates to the sides of existing reinforced concrete beams to strengthen and stiffen them. Unlike standard composite steel and concrete beams in which there is longitudinal-partial-interaction at the steel/concrete interface (that is slip along the length of the beam), composite bolted side-plated reinforced-concrete beams are unique in that they also exhibit transverse-partial-interaction, that is slip transverse to the length of the beam. In this work, the fundamental mathematical models for transverse-partial-interaction and its interaction with longitudinal-partial-interaction are developed. The fundamental models are then further developed to determine the number of connectors required to resist the transverse forces and to limit the degree of transverse-partial-interaction in bolted side-plated reinforced concrete beams.
Key Words
plated beam, partial-interaction, reinforced-concrete beam
Address
Oehlers DJ, UNIV ADELAIDE,DEPT CIVIL & ENVIRONM ENGN,ADELAIDE,SA 5005,AUSTRALIA UNIV NEW S WALES,DEPT STRUCT ENGN,SYDNEY,NSW 2052,AUSTRALIA
Abstract
The material-based homogenization design method generates arbitrary topologies of initial structural design as well as reinforcement structural design by controlling the amount of material available. However, if a small volume constraint is specified in the design of Lightweight structures, thin and slender structures are usually obtained. For these structures stability becomes one of the most important requirements. Thus, to prevent overall buckling (that is, to increase stability), the objective of the design is to maximize the buckling load of a structure. In this paper, the buckling analysis is restricted to the linear buckling behavior of a structure. The global stability requirement is defined as a stiffness constraint, and determined by solving the eigenvalue problem. The optimality conditions to update the design variables are derived based on the sequential convex approximation method and the dual method. Illustrated examples are presented to validate the feasibility of this method in the design of structures.
Abstract
In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or nonequilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.
Key Words
stability, buckling, bifurcation, path-tracing, pinpointing, path-switching, nonlinear solution methods, local iteration
Address
Fujii F, GIFU UNIV,GIFU 50111,JAPAN NAGOYA UNIV,NAGOYA,AICHI 46401,JAPAN
Abstract
A numerical model for masonry is proposed by following an internal variable approach originally developed in the field of elastic-plastic analysis. The general features of the theoretical framework are discussed by focussing on finite element models applicable to incremental elastic-plastic problems. An extremum property is derived and its implications in terms of convergence for convenient algorithms are briefly discussed, by including the case of softening materials and damage effects. Next, a numerical model is presented, which is suitable for masonry, can be developed according to the same internal variable formulation and enjoys similar properties. Some numerical results are presented and compared with the response of a masonry shear wall subjected to pseudodynamic tests.
Abstract
The concrete stiffness matrices of membrane elements used in the finite element analysis of wall-type structures are reviewed and discussed. The behavior of cracked reinforced concrete membrane elements is first described by summarizing the constitutive laws of concrete and steel established for the two softened truss models (the rotating-angle softened-truss model and the fixed-angle softened-truss model). These constitutive laws are then related to the concrete stiffness matrices of the two existing cracking models (the rotating-crack model and the fixed-crack model). In view of the weakness in the existing models, a general model of the matrix is proposed. This general matrix includes two Poisson ratios which are not clearly understood at present. It is proposed that all five material properties in the general matrix should be established by new biaxial tests of panels using proportional loading and strain-control procedures.
Key Words
concrete, constitutive laws, cracking, material matrix, membrane element, Poisson ratio, reinforced concrete, shear, stiffness, stress-strain relationship
Abstract
The optimization of cutouts in composite plates was investigated by implementing a procedure known as Evolutionary Structural Optimization. Perforations were introduced into a finite element mesh of the plate from which one or more cutouts of a predetermined size were evolved. In the examples presented, plates were rejected from around each evolving cutout based on a predefined rejection criterion. The Limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure criterion. Finite element plates with values below the product of the average Tsai-Hill number and a rejection criterion were subsequently removed. This process was iterated until a steady state was reached and the rejection criterion was then incremented by an evolutionary rate and the above steps repeated until the desired cutout area was achieved. Various plates with differing lay-up and loading parameters were investigated to demonstrate the generality and robustness of this optimization procedure.
Abstract
Reinforced concrete (RC) interior beam-column joints with high-strength materials: concrete compressive strength of 100 MPa and the yield strength of longitudinal bars of 685 MPa, were analyzed using three-dimensional (3-D) nonlinear finite element method (FEM). Specimen OKJ3 of joint shear failure type was a plane interior joint, and Specimen 12 of beam flexural failure type was a 3-D interior joint with transverse beams. Though the analytical initial stiffness was higher than experimental one, the analytical results gave a good agreement with the test results on the maximum story shear forces, the failure mode.
Key Words
reinforced concrete, beam-column joints, high-strength materials, shear strength, three-dimensional analysis, finite element method
Abstract
The paper reviews the implementation and evaluation of exact methods for the computation of transcendental structural eigenvalues, i.e., critical buckling loads and natural frequencies of undamped vibration, on multiple instruction, multiple data parallel computers with distributed memory. Coarse, medium and fine grain parallel methods are described with illustrative examples. The methods are compared and combined into hybrid methods whose performance can be predicted from that of the component methods individually. An indication is given of how performance indicators can be presented in a generic form rather than being specific to one particular parallel computer. Current extensions to permit parallel optimum design of structures are outlined.
Key Words
parallel computers, structural analysis, buckling, vibration, optimum design
Abstract
A nonlinear semi-three-dimensional layered finite element procedure is developed for cracking and failure analysis of reinforced concrete beams and the spandrel beam-column-slab connections of flat plates. The layered element approach takes the elasto-plastic failure behaviour and geometric nonlinearity into consideration. A strain-hardening plasticity concrete model and a smeared steel model are incorporated into the layered element formulation. Further, shear failure, transverse reinforcement, spandrel beams and columns are successfully modelled. The proposed method incorporating the nonlinear constitutive models for concrete and steel is implemented in a finite element program. Test specimens including a series of reinforced concrete beams and beam-column-slab connections of flat plates are analysed. Results confirm the effectiveness and accuracy of the layered procedure in predicting both flexural and shear cracking up to failure.
Abstract
Bond-slip behavior between reinforcement and concrete under push-pull cyclic loadings is numerically investigated based on a reinforcement model proposed in this paper. The equivalent reinforcing steel model considering the bond-slip effect without taking double nodes is derived through the equilibrium at each node of steel and the compatibility condition between steel and concrete. Besides a specific transformation algorithm is composed to transfer the forces and displacements from the nodes of the steel element to the nodes of the concrete element. This model first results in an effective use in the case of complex steel arrangements where the steel elements cross the sides of the concrete elements and second turns the impossibility into a possibility in consideration of the bond-slip effect in three dimensional finite element analysis. Finally, the correlation studies between numerical and experimental results under the continuously repeated large deformation stages demonstrate the validity of developed reinforcing steel model and adopted algorithms.