Topology optimization of continuum structures subjected to pressure loading

This paper presents a generalization of topology optimization of linearly elastic continuum structures to problems involving loadings that depend on the design. Minimum compliance is chosen as the design objective, assuming the boundary conditions and the total volume within the admissible design domain to be given. The topology optimization is based on the usage of a SIMP material model. The type of loading considered in this paper occurs if free structural surface domains are subjected to static pressure, in which case both the direction and location of the loading change with the structural design. The presentation of the material is given in a 2D context, but an extension to 3D is straightforward. The robustness of the optimization method is illustrated by some numerical examples in the end of the paper. Received August 3, 1999     

Nonlinear analysis of concrete cylinder structures under hydrostatic loading

The paper reports the recent results of four aspects of nonlinear analysis of concrete cylinder structures under hydrostatic loading—(1) further development of concrete constitutive relationships based on a plasticity formulation; (2) kinematics of failure mode for crushing and cracking concrete; (3) implementing the results in the form of a subroutine suitable for incorporation in a large finite-element analysis computer code (NONSAP program); and (4) studying the behaviour and strength of concrete cylindrical shell structures under hydrostatic pressure.The computer model developed includes the nonlinear displacement and material behaviour which is capable of performing parametric studies on the influence of geometric imperfections, variable restrained end supports, nonlinear nature of stress-strain-fracture response, and the non-conservative nature of hydrostatic loading. Using this computer model, comparisons have been made with the results of tests on actual cylinders, providing the needed confirmation of the validity of the model.     

Analysis and optimal design of layered structures subjected to impulsive loading

The attenuation of elastic stress waves propagating through layered structures situated between free and fixed surfaces is investigated. A stress transfer function, which relates the stress response at the fixed support to the applied stress pulse, is derived for several specific layered structures. An analysis of these responses indicate that when an incident stress pulse passes through a layered structure, a reduced stress amplitude and elongated pulse duration could be obtained with proper selection of materials and layer dimensions. Consequently, a design procedure is proposed to obtain the optimal layered structure, and several specific cases of layered structures are investigated.     

Finite element analysis of reinforced and prestressed concrete structures including thermal loading

This paper describes the application of finite element techniques to the solution of nonlinear concrete problems. Reinforced concrete thick plates and shells are first considered for which both a perfect and strain-hardening plasticity approach are employed to model the compressive behaviour. A dual criterion for yielding and crushing in terms of stresses and strains is considered, which is complemented with a tension cut-off representation. Degenerate thick shell elements employing a layered discretisation through the thickness are adopted and both reduced and selectively integrated 8-node serendipity and heterosis elements are considered.Thermal loading of prestressed concrete structures is also considered which necessitates the inclusion of time effects in the analysis. The technique described in this paper involves concurrently solving an uncoupled set of equations within a time interval to provide both the displacement and temperature increments. A two-level time stepping scheme is employed to predict temperature changes within a time interval and elasto-viscoplastic material analysis is performed using an explicit forward-difference scheme incorporating an equilibrium iteration procedure. The constitutive model for the concrete is essentially identical to that employed for the plate and shell analysis.Numerical examples are presented for both types of analysis and comparison is made with experimental results whenever possible. Additionally, results for thermal loading are presented which indicate that a full transient thermal-mechanical analysis is sometimes essential in order to obtain a realistic structural response.     

The computer aided design of structural concrete sections subjected to combined loading

The paper describes a Computer Subroutine that may be employed to design the reinforcing steel of reinforced and prestressed concrete sections subjected to vertical shear, lateral shear, vertical bending, lateral bending, torsion and axial load. The Subroutine, called DEVAST (Design by the Variable Angle Space Truss) is based on a space truss model that is capable of predicting the post-cracking behavior of rectangular structural concrete sections subjected to combined loading. Since the space truss model can be used to predict the full post-cracking response of concrete beams under combined loading (i.e. strain in the longitudinal and web reinforcement, as well as the various deformations of the beam at all load levels), it is possible to predict the load combination that will result in yielding of either the longitudinal or the hoop steel. As a simple and conservative design criterion for use in Sub-program DEVAST, the reliable capacity of the section is taken as the load corresponding to first yielding of the steel. Although conceived as a Sub-program to be used in conjunction with a Main Program that performs the structural analysis, this Subroutine may very simply be modified for use as a self-contained design program. A listing of Sub-program DEVAST written in FORTRAN IV is provided in the paper.     

On the optimal layout of structures subjected to probabilistic or multiply loading

The loading uncertainties can be expressed by the stochastic nature of any part of the load determination. If any information is probabilistic among the three independent data of the load determination (the magnitude, the line of action and/or the point of application) a more precise design requires to elaborate a probabilistic method. This goal can be obtained by the use of an appropriate approximation technique, in which the original stochastic mathematical programming problem is substituted by a deterministic one. A similar technique can be followed in case of a multiple loading. In addition to the numerical modelling a parametric study is given where the influence of the multiple loading is investigated to determine the optimal layout in function of the initial layout. The application is illustrated by numerical examples.     

Numerical simulation study of spallation in reinforced concrete plates subjected to blast loading

In the design of protective structures, concrete walls are often used to provide effective protection against blast from incidental events. With a reasonable configuration and proper reinforcement, the protective structure could sustain a specified level of blast without global failure. However, the concrete wall may generate spallation on the back side of the wall, posing threats to the personnel and equipment inside the structure. For this concern, it is important to establish appropriate concrete spallation criteria in the protective design. Earlier analytical studies have been based on simplified one-dimensional wave theory, which does not consider the complex three-dimensional stress conditions in the case of close-in explosion and the structural effects. This paper presents a numerical simulation study on the concrete spallation under various blast loading and structural conditions. A sophisticated concrete material model is employed, taking into account the strain rate effect. The erosion technique is adopted to model the spallation process. Based on the numerical results, the spallation criteria are established for different levels of spallation. Comparison of the analytical results with experimental data shows a favorable agreement. It is also shown that the structural effects can become significant for relatively large charge weight and longer distance scenarios.     

Design and sensitivity analysis of dynamical systems subjected to stochastic loading

The paper presents an efficient procedure which allows to carry out reliability-based optimization of linear systems subjected to stochastic loading. The optimization problem is replaced by a sequence of approximate explicit sub-optimization problems that are solved in an efficient manner. Approximation concepts are used to construct high quality approximations of dynamic responses during the optimization process. The approximations are combined with efficient simulation methods to generate explicit approximations of reliability measures in terms of the design variables. The number of dynamic analyses required for the convergence of the design process is reduced dramatically. An efficient sensitivity analysis with respect to the optimization variables and general system parameters becomes possible with the proposed formulation. The sensitivity is evaluated by considering the behavior of the design when the parameters vary within a bounded region. The analysis can identify the degree of robustness of the final design with respect to variations of selected system parameters. A numerical example in terms of a 26-story reinforced concrete building under stochastic earthquake excitation exemplifies the proposed methodology.     

Elasto-plastic contact stress analysis of joints subjected to cyclic loading

Rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading is carried out. An incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis. For the case of the interference fit, the analysis sequentially carries out insertion of the pin and application of the load on the joint, covering possible initiation of separation (and/or yielding) and progressively the receding/advancing contact at the pin-plate interface. Deformations of both the plate and the pin are considered in the analysis. Numerical examples are presented for the case of an interference fit pin in a large plate under remote cyclic tension, and for an interference fit pin lug joint subjected to cyclic loading. A detailed study is carried out for the latter problem considering the effect of change in contact/separation at the pin-plate interface on local stresses, strains and redistribution of these stresses with the spread of a plastic zone. The results of the study are a useful input for the estimation of the fatigue life of joints.     

爆炸载荷下加筋板的动力学性能分析

为提升军舰、潜艇和航空母舰外板的抗爆炸载荷冲击能力,采用Abaqus分析爆炸载荷下材料阻尼、应变率、加筋板的几何构型及加强筋的几何参数对结构动力学性能的影响.结果表明：加筋板相对于平板具有优异的抗爆炸载荷冲击能力;材料的阻尼及应变率对结构动力学性能影响较大;双十字加筋板相对于其他几何构型的加筋板具有更优良的抗爆炸载荷冲击的能力;矩形加强筋截面高宽比对加筋板动力学性能影响较明显,在结构设计中应该根据需求进行合理选择.     

Density-based topological design of structures subjected to water pressure using a parametric loading surface

Topological design of structures has enjoyed a period of steady growth since the publication of a seminal paper by Bendsøe and Kikuchi. Nowadays, topology design can be recognized as a discipline in structural and multidisciplinary optimization with its idiosyncrasies, specific formulations, and solution techniques. A class of problems, known as topological optimization with design-dependent loading (see Rozvany and Prager (1979) for first closed-form solutions and Fuchs and Moses (2000) for semianalytical results) present often some intrinsic obstacles. Such is the case, in particular, in the presence of pressure loads. Indeed, when water pressure is the applied load, the density-based technique seems to run into trouble because not until the structure has converged is there a clear water/material interface where the pressure can be applied. Several authors have proposed solutions, and this paper adds its contribution. We introduce, independent of the material distribution, a parametric loading surface, the shape of which is an additional unknown. Water pressure is applied at this surface as if it were the water/material interface. By doing so, one factually severs the physical link between the smooth pressure surface and the indistinct material distribution. In order to remove any lingering material from the water region, a small elastic modulus E is assumed there. Additional care was exercised for computing the sensitivities as the loading surface meanders through the fixed grid of the finite element model. For this purpose, a smooth transition for E from the water to the material zone is imposed to alleviate any numerical instabilities that may occur in computing the sensitivities of E over the abrupt transition at the loading surface. Several cases, primarily the design of optimal dams, were tested. The method proved very robust and produced crisp water/material interfaces, which coalesced with the loading surfaces.     

Optimal design of structures subjected to time history loading by swarm intelligence and an advanced metamodel

This paper proposes a new metamodeling framework that reduces the computational burden of the structural optimization against the time history loading. In order to achieve this, two strategies are adopted. In the first strategy, a novel metamodel consisting of adaptive neuro-fuzzy inference system (ANFIS), subtractive algorithm (SA), self organizing map (SOM) and a set of radial basis function (RBF) networks is proposed to accurately predict the time history responses of structures. The metamodel proposed is called fuzzy self-organizing radial basis function (FSORBF) networks. In this study, the most influential natural periods on the dynamic behavior of structures are treated as the inputs of the neural networks. In order to find the most influential natural periods from all the involved ones, ANFIS is employed. To train the FSORBF, the input–output samples are classified by a hybrid algorithm consisting of SA and SOM clusterings, and then a RBF network is trained for each cluster by using the data located. In the second strategy, particle swarm optimization (PSO) is employed to find the optimum design. Two building frame examples are presented to illustrate the effectiveness and practicality of the proposed methodology. A plane steel shear frame and a realistic steel space frame are designed for optimal weight using exact and approximate time history analyses. The numerical results demonstrate the efficiency and computational advantages of the proposed methodology.     

A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading

The material point method (MPM) takes advantages of both the Eulerian and Lagrangian methods, so it is capable of handling many challenging engineering problems, such as the dynamic responses of reinforced concrete (RC) subjected to blast and impact loadings. However, it is time-consuming to discretize the steel reinforcement bars (“rebars”) in RC by using MPM because the diameter of the steel bar is very small compared with the size of concrete. A hybrid finite element–material point (FEMP) method is proposed, in which the truss element in the traditional finite element method (FEM) is incorporated into the MPM to model the rebars. The proposed FEMP method is implemented in our three-dimensional material point method code, MPM3D®, and validated by several benchmark problems. Finally, it is applied to simulate the dynamic response of RC slab penetrated by projectile, and the numerical results are in good agreement with the experimental data reported in the literature. The proposed idea is applicable to incorporate other types of finite elements into MPM to take advantages of both FEM and MPM.     

Elastic-plastic-fracture analysis of concrete structures

The paper presents a computer implementation technique for an elastic-plastic-fracture analysis of concrete structures. To this end, the finite element formulation for a fractured concrete element as well as the relevant redistribution procedure of released stresses are described. Further, it is discussed how the finite element method may be applied effectively in the analysis of concrete structures subjected to different types of loading conditions. In particular, in order to avoid the structure-load system interaction during an unstable process of material fracturing, two extreme loading conditions are considered: (1) dead load, and (2) the load applied by a rigid testing machine. This leads in turn to a pure load and a pure displacement-control analysis. Based on the computer program developed, two typical computational examples are presented involving nonlinear progressive collapse analysis of split-cylinder test, and implosion analysis of a concrete cylindrical hull.     

Nonlinear analysis of reinforced concrete structures

For the prediction of yield and failure of concrete under combined stress, a generalization of the Mohr-Coulomb behavior is made in terms of the principal stress invariants. The generalized yield and failure criteria are developed to account for the two major sources of nonlinearity: the progressive cracking of concrete in tension, and the nonlinear response of concrete under multiaxial compression. Using these criteria, incremental stress-strain relationships are established in suitable form for the nonlinear finite element analysis.For the analysis of reinforced concrete members by finite elements, a method is introduced by which the effect of reinforcement is directly included. With this approach, the stress-strain laws for the constituent materials of reinforced concrete are uncoupled permitting efficient and convenient implementation of a finite element program. The applicability of the method is shown on sample reinforced concrete analysis problems.     

受剪复合材料加筋平板筋条剥离分析

为研究筋条-蒙皮界面强度对复合材料加筋平板剪切承载能力的影响,采用基于接触属性定义的粘聚区模型分析蒙皮-筋条界面损伤的萌生和扩展,采用基于二维Hashin准则的渐进损伤模型计算复合材料层板失效.仿真结果与试验吻合较好,验证基于接触属性定义的粘聚区模型用于整体复合材料加筋板筋条剥离分析的工程实用性.计算结果表明:为充分发挥复合材料加筋板的承载潜力,筋条-蒙皮界面应具有较高的强度.     

Computerized ultimate strength analysis of reinforced concrete sections subjected to axial compression and biaxial bending

This article presents a method of evaluating the ultimate strength capacities of reinforced concrete sections of arbitrary shapes and with or without voids subjected to axial compression and biaxial bending. The concept of load fraction is introduced so as to provide a quantitative measure of structural adequacy. An iterative procedure to determine the load fractions is proposed. Necessary integration over arbitrary domains is dealt with by boundary integration method. This procedure can be computerized readily to high automation. A wide range of reinforced concrete sections are analysed, as examples, using a desk-top computer.     

Constrained optimization of structures with displacement constraints under various loading conditions

Optimization problems often involve constraints and restrictions which must be considered in order to obtain an optimum result and the resultant solution should not deviate from any of the imposed constraints. These constraints and restrictions are imposed either on the design variables or on the algebraic relations between them. Constraints of allowable stress, minimum size and buckling of members in the absence of allowable displacement constraint are the most important factors in optimization of the cross-sectional area of structural elements. When the allowable displacement constraint is included in the problem as a determinant parameter, since the specifications of most of elements affect the displacement rate, the way of imposing and considering this constraint requires special care. In this research the way of simultaneous imposition of multi displacement constraints for optimum design of truss structures in several load cases is described. In this method various constraints for different load cases are divided into active and passive constraints. The mathematical formulation is based on the classical method of Lagrange Multipliers. Overall, this simple method can be employed along with other constraints such as buckling, allowable stress and minimum size of members for imposing the displacement constraint in various load cases.     

Failure of Au RF-MEMS switches subjected to dynamic loading

The dynamic failure of Au RF-MEMS was investigated over a wide range of loading rates by three different experimental setups: a drop weight tower, which induced a maximum peak acceleration of 600g (g: acceleration of gravity), a Hopkinson pressure bar with a maximum peak acceleration of 300,000g, and a pulsed laser loading technique with a maximum peak acceleration of 1.8 × 10⁸g. In the drop weight tower the total load pulse duration was in the milliseconds range – much longer than the 28 μs resonant period of the devices – and no failure of any kind occurred in the RF-MEMS devices or their substrate. At 90,000g (generated in the Hopkinson bar) no damage in either the substrate or the devices was observed. However, at 200,000g, which corresponds to a loading duration of a few microseconds, i.e., comparable to the device resonant period, 10% of the switches failed although postmortem imaging showed no damage to the substrate. Damage increased after this acceleration and at 300,000g 20% of the switches failed, but, in addition, significant failure in the quartz substrate was recorded. Lastly, the pulsed laser loading technique, which has a loading pulse duration of a few tens of nanoseconds, was applied to accelerate the Au switches to 1.8 × 10⁸g, and the probability of failure at this loading ranged from 50% to 80%. At even larger accelerations, 10⁹g, the probability of failure was 100%. The results of this study establish the severity of dynamic failure in MEMS, despite their small mass, and its dependence on the level of acceleration which spanned about 7 orders of magnitude.