Damage-reduction-based structural optimum design for seismic RC frames

The development of structural seismic design is briefly reviewed with an emphasis on different conceptual approaches and their success in practical engineering applications. The concept of damage-reduction-based seismic design is proposed, in which the whole structural system is either physically or functionally designed as two parts, the main-function part and the damage-reduction part. The main-function part satisfies the serviceability requirements of the structural system. The damage-reduction part is composed of several damage-reduction elements, which work under hazard loads to ensure the safety of the main-function part, and further maintain the serviceability of the structural system by specific damage-reduction techniques or even by failure of damage-reduction elements. The formulation of damage-reduction-based optimum design for seismic structures is presented and some related issues are addressed, including a simplified approach to reliability analysis, the evaluation of the structural loss expectation, and the modified enumeration method. Numerical examples of RC frames are examined. The results show that several measures of structural seismic performance, including the life-cycle cost, severe earthquake action, and the story-drift reliability index of the weakest story, can be improved by damage-reduction-based design compared with conventional design.     

The behavior of masonry assemblages and masonry-infilled R/C frames subjected to combined vertical and cyclic horizontal seismic-type loading

The present systematic study aims to propose valid numerical models that can realistically approximate the shear behavior of masonry assemblages and the hysteretic behavior of masonry infilled reinforced concrete (R/C) frames when they are subjected to combined vertical and horizontal cyclic loads. Successful numerical simulations are developed for the non-linear shear behavior of masonry joints and the non-linear behavior and ultimate strength of relatively weak Greek masonry piers; these are finally used, with the same materials and geometry, as infills in the R/C frames. A valid numerical model is proposed that can capture successfully the various observed non-linear response mechanisms that develop within the masonry infilled R/C frames when they are subjected to combined vertical and cyclic horizontal loads.     

Numerical analysis of anisotropic rotational shells subjected to nonsymmetric loads

Through the use of an integral transform, the present paper extends the applicability of the multisegment numerical integration technique to include the solution of general macroscopically anisotropic multilayered shells of revolution. It is found that compared with orthotropic shells, material anisotropy induces a doubling in the number of transformed fundamental equations characterizing the static response. Employing the transform together with the multisegment integration technique and several concepts from the direct stiffness method of structural analysis, procedures are developed which can handle branched anisotropic multilayered shells of revolution in a more effective manner than was previously possible. Based on the procedures outlined in the paper, numerical studies are presented which show the effect of segment size on the solution accuracy and the effects of material anisotropy on selected shell configurations.     

Optimal synthesis method for transmission tower truss structures subjected to static and seismic loads

In this study, an efficient optimal synthesis method for determining the optimum solutions for the structural shape, cross-sectional dimensions, and material type of all member elements of large-scale transmission tower truss structures subjected to static and seismic loads is presented. The method is developed by using the dual method, the response spectrum method, suboptimization techniques, and a two-stage optimization process. The example of a cost-minimization problem for a 218-bar transmission tower truss that considers not only the material costs but also the cost of land as objective functions is presented to demonstrate the rigorousness, efficiency, and reliability of the proposed method.     

Numerical problems in modelling of collision in sliding systems subjected to seismic excitations

The study addresses collision in sliding systems subjected to seismic excitations. The collision is modelled according to the impact laws of the mechanics of particles using coefficient of restitution to account for energy losses (Newton's hypothesis). An analytical solution in a small time interval after the collision is constructed viewing the sliding velocity. When constructing numerical solutions, it is assumed that the friction force does not change its sign within one step of integration. If at end of the time step, velocity with an opposite sign is calculated, the obtained solution is incorrect, because the result contradicts the accepted constant sign of the friction force during the time step. To avoid these problems expressions are derived for the magnitude of the time step in which a mathematically correct solution will have place. Recommendations are formulated for numerical simulation of collision in sliding systems subjected to seismic excitations. The obtained correct numerical solutions using the Coulomb model are compared with numerical results from the velocity model of friction forces. It is shown that the velocity model provides the possibility to avoid automatically the above numerical problems by use of its correctness condition.     

Elastic buckling of perforated plates subjected to concentrated loads

Results are presented for concentrated loading applied to perforated plates of different aspect ratios. Two different in-plane restraint conditions and four edge conditions have been analysed. The results have been obtained by the application of the conjugate load/displacement method of elastic stability analysis, and show how simple modifications to plate geometry, particularly with respect to perforation aspect ratio and support conditions, can effect major changes to the elastic critical load.     

Numerical and experimental evaluation of seismic capacity of high-rise steel buildings subjected to long duration earthquakes

Occurrences of large earthquakes having a magnitude larger than eight along subduction zones have been reported worldwide. Due to large number of load reversals the effect of cumulative damage on structural components due to deterioration becomes critical for steel buildings of old construction but may also become critical for buildings designed based on current seismic provisions. A state-of-the-art analytical model that simulates component deterioration and fracture due to low cycle fatigue has been developed and implemented in the OpenSees computational framework. The model serves for seismic evaluation of steel moment frame structures subjected to long duration records. The effectiveness of the numerical model in quantification of the seismic capacity of high rise steel structures is demonstrated through validation with a full scale shaking table test of a high-rise steel building subjected to a long duration record at the world’s largest shaking table facility (E-Defense). Limitations of the proposed numerical model are also discussed.     

Fiber composite thin shells subjected to thermal buckling loads

The results of parametric studies to assess the effects of various parameters on the buckling behavior of angle-ply, laminated thin shells in a hot environment are presented in this paper. These results were obtained by using a three-dimensional finite element analysis. An angle-ply, laminated thin shell with fiber orientation of [θ/ −θ]₂ was subjected to compressive mechanical loads. The laminated thin shell has a cylindrical geometry. The laminate contained T300 graphite fibers embedded in an intermediate-modulus, high-strength (IMHS) matrix. The fiber volume fraction was 55% and the moisture content was 2%. The residual stresses induced into the laminated structure during the curing were taken into account. Parametric studies were performed to examine the effect on the critical buckling load of the following parameters: cylinder length and thickness, internal hydrostatic pressure, different ply thicknesses, different temperature profiles through the thickness of the structure, and different layup configurations and fiber volume fractions. In conjunction with these parameters the ply orientation varied from 0° to 90°. Seven ply angles were examined: 0°, 15°, 30°, 45°, 60°, 75°, and 90°. The results show that the ply angle θ and the laminate thickness had significant effects on the critical buckling load. The fiber volume fraction and the internal hydrostatic pressure had important effects on the critical buckling load. The cylinder length had a moderate influence on the buckling load. The thin shell with [θ/−θ]₂ or [θ/−θ]^s angle-ply laminate had better buckling-load performance than the thin shell with [θ]₄ off-axis laminate. The temperature profiles through the laminate thickness and various laminates with the same thickness but with the different ply thickness had insignificant effects on the buckling behavior of the thin shells.     

A review of optimization of structures subjected to transient loads

Various aspects of structural optimization techniques under transient loads are extensively reviewed. The main themes of the paper are treatment of time-dependent constraints, calculation of design sensitivity, and approximation. Each subject is reviewed with corresponding papers that have been published since the 1970s. The treatment of time-dependent constraints in both the direct method and the transformation method is discussed. Two ways of calculating design sensitivity of a structure under transient loads are discussed—direct differentiation method and adjoint variable method. The approximation concept mainly focuses on the response surface method in crashworthiness and local approximation with the intermediate variables. Especially, a method using the equivalent static load is discussed as an approximation method. It takes advantage of the well-established static response optimization. The structural optimization in flexible multibody dynamic systems is reviewed in the viewpoint of the above three themes.     

Minimum mass design of elastic frames subjected to multiple load cases

For frames with stress- and displacement constraints subjected to multiple load cases the formulation is given that enables use of the unified optimization approach which combines finite element and linear programming. Sensitivity analysis is shown analytically for Timoshenko beam models with transformations for eccentricities. For a specific case of a portal frame for a crane a study is made of the influence of the given portal columns (boundary conditions), the relations to fully stressed designs, and the influence of slenderness, when displacement constraints are involved.     

Probabilistic free vibration analysis of beams subjected to axial loads

A stochastic finite-element-based algorithm for the probabilistic free vibration analysis of beams subjected to axial forces is proposed in this paper through combination of the advantages of the response surface method, finite element method and Monte Carlo simulation. Uncertainties in the structural parameters can be taken into account in this algorithm. Three response surface models are proposed. Model I: star experiment design using a quadratic polynomial without cross-terms; Model II: minimum experiment design using a quadratic polynomial with cross-terms; Model III: composite experiment design using a quadratic polynomial with cross-terms.A separate set of finite element data is generated to verify the models. The results show that the Model II is the most promising one in view of its accuracy and efficiency. Probabilistic free vibration analysis of a simply supported beam is performed to investigate the effects of various parameters on the statistical moments of the frequency response of beams. It is found that the geometric properties of beams have significant effects on the variation of frequency response.     

Optimal design of interference fit assemblies subjected to fatigue loads

This paper presents a methodology for an optimal design of interference fit subjected to fatigue loads. Optimization consists in finding a trade-off between mass and competing safety factors at hub and shaft contact zone as well as in shaft fillet. Developing an effective calculation method for fatigue strength of an interference fitted assembly using the finite element method is one of the main steps of the procedure. Meanwhile, coupling the finite elements model of interference fit with an optimization algorithm is not adequate considering the computing time and the significant number of calculations necessary to portrait the assembly behavior. Therefore, a sequential approximate multi-objective optimization algorithm (SAMOO) is presented. The method involves Design Of Experiments (DOE), interpolation with kriging functions, and multi-objective optimization. Preliminary study of parameter variance, and advanced post-processing of multi-objective optimization, provide engineers with valuable information for identifying an optimal design of interference fit assembly using fewer finite element calculations.     

Series solutions of structural systems subjected to static and dynamic loads

Solutions of complex structural systems for general boundaries are intractable in closed-form through the classical techniques. However, such structural systems have been analyzed herein with the aid of fast converging Fourier Series solution techniques and the macro flexibility concepts. Specifically, the one- and two-dimensional structural systems under static and dynamic loads have been analyzed. In addition, approximate design formulae for forces and displacements have been developed and validated through the results obtained from other existing techniques.The proposed methodology appears to be direct and lends itself well to solving two-dimensional static and dynamic problems with general boundaries. Also, it is well-suited to arriving at one- and two-term approximations for displacements, forces and eigen values. These values are within a 10% range of the “EXACT” values. For example, displacements of skewed plates from the proposed solution are not only accurate but converge with the decreasing skewed angle.The work presented herein is a summary of the sponsored research applied to practical structural systems. Structural idealizations to physical systems are suggested herein. Simple design formulae are presented for use by the practicing structural engineer.     

Optimal design of elasto-plastic structures subjected to normal and extreme loads

When in the design of structures extreme loadings such as short time, high intensity dynamic pressure (explosion), impact or earthquake have to be taken into consideration then, except for special cases, the plastic reserves of the material can be utilized, but the development of excessive plastic deformations, residual displacements and the collapse have to be prevented. Following this design concept in this paper three appropriate methods are presented for the determination of the optimal layout of material of elasto-plastic structures (beams, frames, trusses and plates) subjected to extreme loading. The investigation is extended also to the case when in the optimal design in addition to one of the extreme loads the normal (working) loads can be separately or simultaneously taken into consideration.     

Dynamic stability of short cantilever columns subjected to distributed axial loads

Dynamic stability of short cantilever columns subjected to two types of distributed loads are investigated by using a finite element formulation. Buckling load parameters and frequency parameters bounding the instability regions are presented for various slenderness ratios.     

Low cost analysis of building frames for lateral loads

A new rational method for the analysis of plane frame by microcomputer is presented. The distribution of the vertical and rotational displacements at the nodes of a story is characterised by the concept of distribution factors which are relative nodal displacements. The distribution factors are allowed to vary from floor to floor and are determined by using three floors at a time. These are calculated once only for floors having identical members. By means of the distribution factors, the number of degrees of freedom is reduced to three at any one floor. Therefore, it is possible for a micro—computer to handle a large number of stories without difficulty. The resulting displacements and internal forces compared very well with full finite element analyses for a number of cases even with sudden changes of stiffness. The method should find applications in other regular structures with arbitrary stiffness distributions.     

Topology optimization framework for structures subjected to stationary stochastic dynamic loads

The field of topology optimization has progressed substantially in recent years, with applications varying in terms of the type of structures, boundary conditions, loadings, and materials. Nevertheless, topology optimization of stochastically excited structures has received relatively little attention. Most current approaches replace the dynamic loads with either equivalent static or harmonic loads. In this study, a direct approach to problem is pursued, where the excitation is modeled as a stationary zero-mean filtered white noise. The excitation model is combined with the structural model to form an augmented representation, and the stationary covariances of the structural responses of interest are obtained by solving a Lyapunov equation. An objective function of the optimization scheme is then defined in terms of these stationary covariances. A fast large-scale solver of the Lyapunov equation is implemented for sparse matrices, and an efficient adjoint method is proposed to obtain the sensitivities of the objective function. The proposed topology optimization framework is illustrated for four examples: (i) minimization of the displacement of a mass at the free end of a cantilever beam subjected to a stochastic dynamic base excitation, (ii) minimization of tip displacement of a cantilever beam subjected to a stochastic dynamic tip load, (iii) minimization of tip displacement and acceleration of a cantilever beam subjected to a stochastic dynamic tip load, and (iv) minimization of a plate subjected to multiple stochastic dynamic loads. The results presented herein demonstrate the efficacy of the proposed approach for efficient multi-objective topology optimization of stochastically excited structures, as well as multiple input-multiple output systems.

     

Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm

In this paper, the seismic design of reinforced concrete (RC) frames subjected to time-history loadings was formulated as an optimization problem. Because finding the optimum design is relatively difficult and time-consuming for structural dynamics problems, an innovative algorithm combining multi-criterion decision-making (DM) and Particle Swarm Optimization (PSO), called DMPSO, was presented for accelerating convergence toward the optimum solution. The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete optimization problems. The main goal was to minimize the cost or weight of structures subjected to time-history loadings while satisfying all design requirements imposed by building design codes. The results confirmed the ability of the proposed algorithm to find the optimal solutions for structural optimization problems subjected to time-history loadings.     

随机及移动荷载激励下弹性梁分岔与混沌

移动荷载通过简支梁时,粗糙的梁表面会使移动荷载转变为随机激励.本文考虑梁的几何非线性因素,基于随机Melnikov理论确定了系统在均方意义下发生异宿分岔以及混沌的边界条件.利用数值随机Runge-Kutta方法对随机激励和周期激励共同作用下的系统响应进行了仿真计算,最大Lyapunov指数等数值结果描述了动力学行为变化过程.结果表明当荷载的速度一定时,梁跨中的非线性动力学行为受到质量和随机激励的共同影响,表面平整度较差的梁会增加混沌产生的可能性.