Weight optimization of stiffened cylinders under axial compression

A procedure is developed for the design of a stiffened cylinder under a given uniform axial compression with minimum weight. The approach allows the consideration of various shapes of stiffening members. The effective stiffness of the skin in its post-buckled state is taken into account in the basic analysis. The buckling analyses are accomplished as a minimum problem in the buckling mode shape parameters space using the variable metric method. A mixed procedure which combines the exterior penalty function concept and random search is used to minimize the weight of the stiffened cylinders. The design examples demonstrate the validity of the present approach.     

Application of genetic algorithm to optimization of buckling restrained braces for seismic upgrading of existing structures

A systematic methodology is proposed for determining the optimal cross-sectional areas of buckling restrained braces used for the seismic upgrading of structures against severe earthquakes. Single-objective and multi-objective optimization problems are formulated. The objective for the former is cost and those for the latter are cost and damage. The constraint is the minimum structural performance required. A genetic algorithm is employed to solve both types of problem. Performance is estimated by conducting nonlinear dynamic analysis. A preliminary procedure based on static analysis is adopted to improve the search efficiency. Both approaches are applied to the strengthening of a multi-storey frame.     

Vibration and buckling analysis of plates of abruptly varying stiffness

The application of B-spline functions and the Rayleigh-Ritz procedure to analyze vibration and buckling of plates with abruptly varying stiffnesses is presented. Numerical examples of stepped thickness plates and perforated plates are presented and the results are discussed in comparison with those of other approximate methods.To demonstrate the versatility of the present method, vibration and buckling of skew plates of stepped thickness are also studied for various skew angles, ratios of thickness and ratios of width.     

Elasto-plastic buckling of stiffener plates in beam-to-column flange connections

The problem of plastic buckling of steel plates is reviewed in relation to the load carrying capacity of stiffener plates in beam-to-column flange connections. Due to the non-uniformity of the stress distribution in these plates, the finite element method is used to compute the stresses in the elastic and plastic ranges. A bifurcation analysis is performed using both flow and deformation theory to evaluate the elasto-plastic buckling of the stiffener. A scaled inverse iterative version of the power method is employed to evaluate the bifurcation load. A parametric study is conducted on stiffeners and design curves are obtained showing the relationship between the critical stress and the slenderness ratio for different plate aspect ratios.     

Maximization of buckling load of laminated composite plates with central circular holes using MFD method

This paper addresses optimal design of simply supported symmetrically laminated composite plates with central circular holes. The design objective is the maximization of the buckling load, and the design variable is considered as the fiber orientation. The first-order shear deformation theory is used for the finite element analysis. The study is complicated because the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used to solve the optimization problems. Finally, the effect of different number of layers, boundary conditions, width-to-thickness ratio, plate aspect ratios, hole daimeter-to-width ratio, and load ratios on the results is investigated.     

Analysis and optimum design of fibre-reinforced composite structures

The optimal design of a carbon-fibre-reinforced plastic (CFRP) sandwich-like structure with aluminium (Al) webs is addressed. The material parameters are determined using tensile tests, whereafter the results of an analytical model, a numerical model and an experimental setup are compared. The analytical and numerical approximations are then used to optimize the structure in a multi-algorithm approach for minimum cost and maximum stiffness. The selected algorithm and approximation are motivated by their accuracy and computational efficiency. The CFRP plates are optimized with respect to ply arrangement, while the complete sandwich-like structure is optimized with respect to the combination of manufacturing and material cost. Design constraints on maximum deflection of the total structure, buckling of the CFRP composite plates, buckling of the Al webs, stress in the composite plates and stress in the Al stiffeners are included in the formulation. For the different phases in the optimization process, we use the recently proposed particle swarm optimization algorithm, a dynamic search technique and a continuous-discrete optimization technique .     

A practical method for the minimum weight design of stiffened plates under uniform lateral pressure

A method for the plastic analysis and minimum weight design of grillages and orthogonally stiffened plates subjected to lateral uniform pressure, and under a varying degree of rotational restraint at the supports, is presented. A computer aided design procedure for orthogonally stiffened rectangular plates based on this method is also described. This includes two optimization stages: overall optimization, in which the plastic moments for the beam in each set are found, and stiffener optimization, in which the optimum stiffener geometry is obtained. This design methodology has proved to be very efficient and easy to apply, and it is particularly valuable in the case of ship structures, where the maximum total number of panel stiffeners is in general not large.     

Optimum weight design of composite laminated plates

Optimum designs for the minimum weight of composite laminated plates subjected to size, displacement, buckling and natural frequency constraints are investigated by a technique of combining finite element method and mathematical programming, in which the structural analysis is based on the YNS theory. The recurrence relation based on the feasible direction method (FDM) and the scaling step is used to modify the design variables (ply-thicknesses and ply-orientations) during the iterative procedure. Grouping technique is engaged in the procedure in order that the number of design variables can be greatly reduced to make the problem more practical. Illustrative examples are given to show that the present technique is quite efficient and reliable.     

Post-buckling behaviour of moderately thick cylindrically orthotropic annular plates

A finite element formulation including the effects of shear deformation and cylindrically orthotropic material properties is described for studying the post-buckling behaviour of annular plates. Numerical results for the buckling load parameter and ratios of nonlinear load parameter to buckling load parameter for various values of orthotropic properties, thicknesses and radii ratios of the plates are presented.     

Weight optimization of stiffened cylinders under axial compression

A methodology is developed, by which one may design a stiffened cylinder of specified material, radius, and length, such that it can safely carry a given uniform axial compression with minimum weight. The solution procedure is divided into two stages, Phase I and Phase II. In Phase I, an unconstrained minimization is performed against one of the active constraints (in this paper-general instability) and data are generated in a sufficiently large region of the design space by employing efficient mathematical search techniques, in Phase II, these data are employed to arrive at the minimum weight configuration that satisfies all other constraints. Two design examples are presented which demonstrate the methodology.     

Buckling load enhancement of damaged composite plates under hygrothermal environment using unified particle swarm optimization

Optimization with Unified Particle Swarm Optimization (UPSO) method is performed for the enhancement of buckling load capacity of composite plates having damage under hygrothermal environment which has received little or no attention in the literature. Numerical results are presented for effect of damage in buckling behavior of laminated composite plates using an anisotropic damage model. Optimized critical buckling temperature of laminated plates with internal flaw is computed with the fiber orientation as the design variable by employing a UPSO algorithm and results are compared with undamaged case for various aspect ratios, ply orientations, and boundary conditions. FEM formulation and programming in the MATLAB environment have been performed. The results of this work will assist designers to address some key issues concerning composite structures. It is observed that the degradation of buckling strength of a structural element in hygrothermal environment as a result of internal flaws can be avoided to a large extent if we use these optimized ply orientations at design phase of the composite structure. This specific application proves the contribution of present work to be of realistic nature.     

Optimization of the buckling load for composite structures taking thermal effects into account

This paper deals with optimization of the buckling load for laminated composite structures. A new methodology has been developed where thermal residual stresses introduced in the manufacturing process are included in the buckling analysis. The thermal effects are also included in the calculation of the buckling load sensitivities, and it is therefore possible to “tailor” the thermal residual stresses in order to increase the buckling load. Rectangular plates and circular cylindrical shells subjected to axial compression are considered. The structures are optimized twice; the first time the thermal residual stresses are ignored in the optimization, and the second time the thermal residual stresses are included in the optimization. These two sets of optimizations give two important results. Firstly, it is possible to increase the buckling load for the structures significantly when the thermal residual stresses are taken into account. Secondly, structures which have been optimized ignoring the effects of thermal residual stresses, may have a buckling load which is much less than expected when the effects of the thermal residual stresses are included. Received November 7, 1999     

A computational methodology to select the best material combinations and optimally design composite sandwich panels for minimum cost

A procedure to select the best material combination and optimally design sandwich laminates with fibre reinforced skins and low density cores for minimum cost is described. Sandwich constructions generally provide improved stiffness/mass ratios and provide more tailoring opportunities than monolithics, and thus greater chance of satisfying design constraints. The objective of the optimisation is to minimise the laminate cost by selecting the skin and core material combination, layer thicknesses and skin fibre angles optimally, subject to load and mass constraints. As the optimisation problem contains a number of continuous (ply angles and thicknesses) and discrete (material combinations) design variables, a sequential solution procedure is devised in which the optimal variables are computed in different stages. The methodology and its benefits are demonstrated using graphite, glass or kevlar/epoxy facings, and balsa or PVC cores.     

On the design of three-ply nonlinearly elastic composite plates with optimal resistance to buckling

The optimal design of symmetric three-ply sandwich plates is studied in the context of finite deformation incompressible nonlinear elasticity. The overall shape of the plate is dictated, fixed amounts of two materials are at our disposal, and performance is defined solely in terms of resistance to buckling. The problem is characterized by three parameters: the volume ratio of the two materials, the stiffness ratio of the two (neo-Hookean) materials, and one of the aspect ratios of the plate. Two competing constructions are considered: one in which the stiffer material is used in the outer plies and the other in which the stiffer material is used for the central ply. It is found that if the material volume ratio and the material stiffness ratio are fixed, then there is a single aspect ratio dependent transition in the optimal design. The configuration with the stiffer material used for the central ply is the optimal design for plates that are sufficiently short in the direction of thrust, while the configuration with the stiffer material used for the outer plies is the optimal design for plates that are sufficiently long in the direction of thrust.     

Optimization of prestressed concrete solid and voided slabs

A methodology is presented for the minimum cost optimization of prestressed concrete solid and voided slabs. Apart from the rationale imparted to the design process, the method is shown to yield considerable savings in prestressing steel and therefore savings in energy. Computer programs developed for the implementation of the methodology have facilitated the speedy running of the procedure a myriad of times over a wide range of design parameters such as span, live load, material and erection cost ratios, concrete and strand strengths, prestress effectiveness etc. Qualitative and quantitative conclusions regarding the behavioural characteristics of the parameters and the manner of their interplay in the optimal picture are advanced.     

Forecasting Financial Failure of Firms via Genetic Algorithms

Given a wide amount of possible ratios available for constructing a LOGIT model for forecasting bankruptcy, this paper provides a computational search methodology, only guided by data, for selecting the financial ratios employed in the model. This procedure is based on genetic algorithms which are used to explore the universe of models made available by all possible existing financial ratios (with very redundant information). This search process of the correct model is guided by the Schwarz information criterion. As an empirical illustration, the methodology is applied to forecasting the failure of firms in the Spanish building industry using annual public accounting information.     

Two approaches for truss topology optimization: a comparison for practical use

This paper discusses ground structure approaches for topology optimization of trusses. These topology optimization methods select an optimal subset of bars from the set of all possible bars defined on a discrete grid. The objectives used are based either on minimum compliance or on minimum volume. Advantages and disadvantages are discussed and it is shown that constraints exist where the formulations become equivalent. The incorporation of stability constraints (buckling) into topology design is important. The influence of buckling on the optimal layout is demonstrated by a bridge design example. A second example shows the applicability of truss topology optimization to a real engineering stiffened membrane problem.     

Optimum design of composite laminates for minimum thickness

In this study, an optimization procedure is proposed to minimize thickness (or weight) of laminated composite plates subject to in-plane loading. Fiber orientation angles and layer thickness are chosen as design variables. Direct search simulated annealing (DSA), which is a reliable global search algorithm, is used to search the optimal design. Static failure criteria are used to determine whether load bearing capacity is exceeded for a configuration generated during the optimization process. In order to avoid spurious optimal designs, both the Tsai–Wu and the maximum stress criteria are employed to check static failure. Numerical results are obtained and presented for different loading cases.     

The effect of aspect ratio on the elastoplastic response of stiffened plates loaded in uniaxial edge compression

A numerical study of the effect of aspect ratio on the buckling and collapse behaviour of flatbar-stiffened plates in compression is described. The plate equations are expressed in finite difference form and the solution is obtained using a dynamic relaxation algorithm. Initial imperfections and residual stresses are also introduced in the study. It was found that, for aspect ratios between 2 and 3.5, buckling occurs in the elastic regime, with the panels exhibiting significant post-buckling strength prior to collapse. For aspect ratios between 1 and 2 buckling occurs as the plastic zone increases, followed by rapid unloading as the panel collapses suddenly. The ultimate strength of the panel reduces with increasing aspect ratio, remaining practically constant at higher aspect ratios. The latter is attributed to the initial single half-wave distortion profile that prohibits the formation of the preferred buckling mode.     

Mixed elements in the optimal design of plates

The theory of design sensitivity analysis of structures, based on mixed finite element models, is developed for static, dynamic and stability constraints. The theory is applied to the optimal design of plates with minimum weight, subject to displacement, stress, natural frequencies and buckling stresses constraints. The finite element model is based on an eight node mixed isoparametric quadratic plate element, whose degrees of freedom are the transversal displacement and three moments per node. The corresponding nonlinear programming problem is solved using the commercially available ADS (Automated Design Synthesis) program. The sensitivities are calculated by analytical, semi-analytical and finite difference techniques. The advantages and disadvantages of mixed elements in design optimization of plates are discussed with reference to applications.