Optimization of retaining wall design using evolutionary algorithms

This paper explores the performance of three evolutionary optimization methods, differential evolution (DE), evolutionary strategy (ES) and biogeography based optimization algorithm (BBO), for nonlinear constrained optimum design of a cantilever retaining wall. These algorithms are based on biological contests for survival and reproduction. The retaining wall optimization problem consists of two criteria, geotechnical stability and structural strength, while the final design minimizes an objective function. The objective function is defined in terms of both cost and weight. Constraints are applied using the penalty function method. The efficiency of the proposed method is examined by means of two numerical retaining wall design examples, one with a base shear key and one without a base shear key. The final designs are compared to the ones determined by genetic algorithms as classical metaheuristic optimization methods. The design results and convergence rate of the BBO algorithm show a significantly better performance than the other algorithms in both design cases.     

Buckling analysis of imperfect frames using a stochastic finite element method

A stochastic finite element method is developed for the buckling analysis of frames with random initial imperfections, uncertain sectional and material properties. The random geometrical imperfections of the frames are described by member initial crookednesses which are modeled as given initial displacement functions with amplitudes treated as random variables. The effects of the random initial geometric imperfections are formulated as a set of equivalent random nodal coordinates in the finite element discretization of the members. The mean-centered second-order perturbation technique is used to formulate the stochastic finite element method for the buckling analysis of the imperfect frames. Use of the present method is illustrated by several examples of buckling analysis of random frames. Results derived from the Monte Carlo method are also obtained for comparison.     

Static stress analysis of a composite bevel gear using a three-dimensional finite element method

The possibility of using composite materials for power transmission spur gear, from a static strength point of view, have been proved by the authors in their previous study. In this present work an attempt has been made to study the behaviour of composite bevel gear from a static load point of view using a three-dimensional finite element method. The performance of two composite material bevel gears are presented and compared with a carbon steel gear. From a static strength point of view a glass epoxy bevel gear is slightly closer to a carbon steel bevel gear than a boron/epoxy bevel gear; but from a displacement point of view glass/epoxy deviates from that of carbon steel much more than boron/epoxy, unlike the case of a composite spur gear, where boron/epoxy was better both from strength and displacement points of view. Hence from the results it is concluded that composite materials such as boron/epoxy can be very much thought of as a material for power transmission bevel gears.     

Shape sensitivity analysis using the indirect boundary element method

The paper describes a novel formulation for the computation of the design sensitivities required for shape optimization problems using the indirect boundary element method. As a first stage, the system of equations that evaluate the fictitious traction sensitivities is differentiated with respect to shape design variables. The stress or displacement sensitivities are then evaluated by direct substitution of the fictitious traction sensitivities into the differentiated stress or displacement kernels. Two other finite difference-based techniques for the evaluation of the stress sensitivities, using the indirect boundary element method are also presented. The advantages and the drawbacks of each approach are discussed. These methods have been shown to be effective, accurate and can be incorporated in an existing BE code with much less programming effort than other BE-based techniques. The efficiency of the three methods is illustrated by optimizing the shape of a 90° V-notch. In all cases, convergence is achieved within three to four iterations.Various approximate techniques are suggested to minimize the computation cost of the optimization problem. These techniques are based on the fundamental features of the stress field, the differentiated kernels and the system of matrices of the optimization problem. Investigations have shown that employing these techniques yields more than a 50% reduction in computer time with insignificant loss of accuracy.     

Nonlinear analysis of skew plates using the finite element method

In this paper finite element analysis of the large deflection behaviour of skew plates has been done. A high precision conforming triangular plate bending element has been used. The central deflection, bending and membrane stresses have been reported for simply supported and clamped rhombic plates. The variations of these quantities have been studied for different skew angles.     

A robust predictive model for base shear of steel frame structures using a hybrid genetic programming and simulated annealing method

This study presents a new empirical model to estimate the base shear of plane steel structures subjected to earthquake load using a hybrid method integrating genetic programming (GP) and simulated annealing (SA), called GP/SA. The base shear of steel frames was formulated in terms of the number of bays, number of storey, soil type, and situation of braced or unbraced. A classical GP model was developed to benchmark the GP/SA model. The comprehensive database used for the development of the correlations was obtained from finite element analysis. A parametric analysis was carried out to evaluate the sensitivity of the base shear to the variation of the influencing parameters. The GP/SA and classical GP correlations provide a better prediction performance than the widely used UBC code and a neural network-based model found in the literature. The developed correlations may be used as quick checks on solutions developed by deterministic analyses.     

Stability analysis for plates using the multivariable spline element method

The multivariable spline element method is used in this paper to solve the stability problems of plates and beams. The bicubic spline functions are employed to construct the bending moments, twisting moments and transverse displacements field. The spine eigenvalue equations with multiple variables are derived based on the Hellinger-Reissner mixed variational principle. Some numerical examples are given, the results are good agreement with other methods.     

Finite element analysis of triangular fins attached to a thick wall

Heat conduction in an array of triangular fins with an attached wall is modeled using the finite element method. An adaptive mesh refinement technique is developed giving accuracy comparable to uniform mesh refinement and much increased computational efficiency. The effects of wall thickness and fin spacing are examined for various Biot numbers. It is shown that for low Biot numbers (Bi < 0.1), the one-dimensional assumption is valid but for higher Biot numbers (Bi 0.1), two-dimensional heat conduction must be considered, temperature distributions at the fin root are always non-uniform and the fin is found not to be effective.     

Shape and topology optimization for closed liquid cell materials using extended multiscale finite element method

A new multiscale shape and topology optimization method is presented to design closed liquid cell materials based on the extended multiscale finite element method, which directly captures the small scale features to the large scale computation. The multiscale optimization method firstly focuses on seeking the optimum geometrical parameters and volume expansion of the fluid in the closed liquid cells in the microscale level in terms of maximizing the macroscale mechanical response of the structure. Furthermore, a new hierarchical multiscale optimization method is developed to optimize the macroscale distributions of closed liquid cells and the microscale shape of the fluid inclusion in the cells. In the macroscale level of the multiscale optimization method, the macroscale design domain is discretized by the multiscale coarse elements, while the shape of the fluid inclusions is set to be the design parameters in the microscale level. This method is firstly utilized to minimize the system compliance of the closed liquid cell structure. Moreover, due to the fact that non-uniform volume expansions of the fluid in cells can induce the elastic action, the multiscale optimization method is further extended to design biomimetic compliant actuators of the closed liquid cell materials. The multiscale optimization methods developed are implemented in the FE-package SiPESC, and the numerical examples are carried out to validate the accuracy of the methods proposed.     

Elasto-plastic analysis of single-angle bolted-welded connections using the finite element method

The results of an extensive numerical elaslo-plastic study of single-angle connections subjected to cyclic loading consisting of end shear and bolt-moment are discussed. The thrust of the study is directed towards an improved understanding of the stress variations and the propagation of plastic zones in the vicinity of the weld.     

A Large scale finite element analysis using domain decomposition method on a parallel computer

A parallel finite element analysis based on a domain decomposition technique (DDT) is considered. In the present DDT, an analysis domain is divided into a number of smaller subdomains without overlap. Finite element analyses of the subdomains are performed under the constraint of both displacement continuity and force equivalence among them. The constraint is satisfied through iterative calculations based on either the Uzawa algorithm or the Conjugate Gradient (CG) method. Owing to the iterative algorithm, a large scale finite element analysis can be divided into a number of smaller ones which can be carried out in parallel.

The DDT is implemented on a parallel computer network composed of a number of 32-bit microprocessors, transputers. The developed parallel calculation system named the ‘FEM server type system’ involves peculiar features such as network independence and dynamic workload balance.

The characteristics of the domain decomposition method such as computational speed and memory requirement are first examined in detail through the finite element calculations of homogeneous or inhomogeneous cracked plate subjected to a tensile load on a single CPU computer.

The ‘speedup’ and ‘performance’ features of the FEM server type system are discussed on a parallel computer system composed of up to 16 transputers, with changing network types and domain decompositions. It is clearly demonstrated that the present parallel computing system requires a much smaller amount of computational memory than the conventional finite element method and also that, due to the feature of dynamic workload balancing, high performance (over 90%) is achieved even in a large scale finite element calculation with irregular domain decomposition.     

Error analysis of a Galerkin method to solve the forward problem in MEG using the boundary element method

Sources of brain activity, e.g. epileptic foci, can be localized with Magnetoencephalography (MEG) measurements by recording the magnetic field outside the head. For a successful surgery a very high localization accuracy is needed. The most often used conductor model in the source localization is an analytic sphere, which is not always adequate, and thus a realistically shaped conductor model is needed. In this paper we examine a Galerkin method with linear basis functions to solve the forward problem in MEG using the boundary element method. Its accuracy is compared to the collocation method with constant and linear basis functions. The accuracies are determined for a unit sphere for which analytic solutions are available. The Galerkin method gives a clear improvement in the accuracy of the forward problem especially for the tangential component of the magnetic field. At realistic MEG measurement distances from the brain the Galerkin method reaches a given accuracy with lower computational costs than the collocation methods starting from a few hundreds of unknowns. With larger meshes the difference for the Galerkin method increases significantly.     

A new strategy for stress analysis using the finite element method

In this paper the authors examine the effectiveness of the Powell-Toint strategy for evaluating the Hessian of the potential energy surface of a finite element model that can be used for linear stress analysis and transient response predictions of structures. Cases for which the Powell-Toint strategy may be cost-effective with the conventional method of stress analysis are identified.     

Flexural analysis of reinforced fibrous concrete members using the finite element method

A numerical procedure based on the finite element method is developed for the geometric and material nonlinear analysis of reinforced concrete members containing steel fibres and subjected to monotonic loads. The proposed procedure is capable of tracing the displacements, strains, stresses, crack propagation, and member end actions of these structures up to their ultimate load ranges. A frame element with a composite layer system is used to model the structure. An iterative scheme based on Newton-Raphson's method is employed for the nonlinear solution algorithm. The constitutive models of the nonlinear material behaviour are presented to take into account the nonlinear stress-strain relationships, cracking, crushing of concrete, debonding and pull-out of the steel fibres, and yielding of the reinforcement. The geometric nonlinearity due to the geometrical change of both the structure and its elements are also represented. The numerical solution of a number of reinforced fibrous concrete members are compared with published experimental test results and showed good agreement.     

Uncertainty analysis on process responses of conventional spinning using finite element method

Conventional spinning is a widely used metal forming process to manufacture rotationally axis-symmetric and asymmetric products. Considerable efforts have been made to investigate the forming quality of spun parts using the process in recent years. However, inherent uncertainty properties involved in the spinning process are rarely considered in previous studies. In this paper, an uncertainty analysis and process optimisation procedure have been developed and implemented on conventional spinning with 3D Finite Element Method (FEM). Three process variables are randomized by Gaussian distribution to study the probabilistic characteristics of two process responses. Linear and quadratic approximate representations are constructed by Monte Carlo based Response Surface Method (RSM) with Latin Hypercube Sampling (LHS). The Most Probable Point (MPP) method, which has been widely used to estimate the failure probability in other applications, is further developed in this paper to obtain the probability distribution of the system responses. Following an evaluation of the system responses conducted by the MPP method, a control variable method is used to reduce the variance of spun part wall thickness and total roller force to satisfy the 3σ quality requirement. This uncertainty analysis and process optimisation procedure can be easily implemented in other metal spinning processes.     

Bending analysis of rectangular moderately thick plates using spline finite element method

A bending analysis of rectangular, moderately thick plates with general boundary conditions is presented using the spline element method. The cubic B spline interpolate functions are used to construct the field function of generalized displacements w, φ_itxand φ_ity. The spline finite element equations are derived based on the potential energy principle. For simplicity, the boundary conditions, which consist of three local spline points, are amended to fit specified boundary conditions. The shear effect is considered in the formulations. A number of numerical examples are described for rectangular, moderately thick plates. Since the cubic B spline interpolate functions have sufficient continuity and are piecewise polynomial, so the present numerical solutions show not only that the method gives accurate results, but also that the unified solutions of thick and thin plates can be directly obtained; the trouble with the so-called shear locking phenomenon does not occur here.     

Computer aided design of a three-dimensional steel frame

This paper describes the sequence of events leading to the successful construction of a three dimensional welded and bolted steel frame which formed the structural support for the floors and roof of a church in Mt. Washington, Ohio. The structure was conceived, planned, designed and checked using the concept of computer aided design by means of ICES-STRUDL. The paper illustrates analysis, design, construction and shows the completed structure. The architectural concept was based on the structural system. Itwas conceived jointly by the architect and the structural engineer as a working team prior to the job competition.The preliminary design and its necessary analysis was performed during this conceptual stage at which time it was determined that the proposed system was feasible with respectto aesthetics, with respect to construction and costs, as well as with respect to being capable of proper analysis and design. The final design was then accomplished by both planar frame assumptions and space frame assumptions, where proper releases were employed in both analyses to account for the designer's best estimation of the actual behavior of the physical joints and connections. This was handled by ICES STRUDL-I on the IBM 360/365 digital computer using the capabilities of loading combinations, joint releases, section properties, deformation values, etc. The lack of accuracy of such an elastic and linear structural computer package is also briefly documented. It is relevant with respect to the actual connections in field construction. The framed structure was actually controlled by deflection criteria, although said criteria was not actually provided by the specifications per se, but rather by the psychological aspects of observable sway. Since this was a highly indeterminate and complex space frame, the interaction of member properties, joint framing, analysis, member checks with respect to specifications, and deformation could only have been successfully satisfied by means of a computer aided process.The main theme is the use of computer-aided design techniques in the planning stage and the preliminary design stage, where it was mandatory to determine the general feasibility of the overall system so that the architectural presentation could be accurately portrayed. An above normal degree of accuracy was also essential in the final design checks and thus a computer oreinted design process was essential to the successful execution of this type of structural system and its integration a priori into the architectural system.     

Transient thermal analysis of underground power cables using two dimensional finite element method

Microsystem Technologies - This paper introduces the finite element method is used for predicting the temperature distribution in underground cable, using arch-shaped finite elements with...     

Solving Wick-stochastic water waves using a Galerkin finite element method

A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water free surface or in the bottom topography among others. To perform a rigorous study of stochastic effects in the shallow water equations we employ techniques from Wick calculus. The differentiation respect to time and space along with the product operations are performed in a distribution sense. Using the Wiener-Itô chaos expansion for treating the randomness, the governing equations are transformed into a sequence of deterministic shallow water equations to be solved for each chaos coefficient by standard methods from computational fluid dynamics. In our study, we formulate a finite element method for spatial discretization and a backward Euler scheme for time integration. Once the chaos coefficients are obtained, statistical moments for the stochastic solution are carried out. Numerical results are presented for stochastic water waves in the Strait of Gibraltar.