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The structural optimization presented in this paper is based on an evolutionary procedure, developed recently, in which the low stressed part of a structure is removed from the structure step‐by‐step until an optimal design is obtained. Various tests have shown the effectiveness of this evolutionary procedure. The purpose of this paper is to present applications of such an evolutionary procedure to the optimal design of structures with multiple load cases or with a traffic (moving) load.

The aim of this paper is to present a novel multifactor structural optimisation method incorporating reliability performance.

This research addresses structural optimisation problems in which the design is required to satisfy multiple performance criteria, such as strength, stiffness, mass and reliability under multiple loading cases simultaneously. A MOST technique is extended to accommodate the reliability‐related optimisation. Structural responses and geometrical sensitivities are analysed by a FE method, and reliability performance is calculated by a reliability loading‐case index (RLI). The evaluation indices of performances and loading cases are formulated, and an overall performance index is presented to quantitatively evaluate a design.

The proposed method is applicable to multi‐objective, multi‐loading‐case, multi‐disciplinary and reliability‐related optimisation problems. The applications to a star‐like truss structure and a raised‐access floor panel structure confirmed that the method is highly effective and efficient in terms of structural optimisation.

A systematic method is proposed. The optimisation method combines the MOST technique with a RLI (a new alternative route to calculate the reliability index at multiple loading cases) using a parametric FE model.

The structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the optimization tool for both.

The topology optimization problem, which is ill posed, is regularized using a constraint on perimeter and solved using GA. The problem is formulated as one of compliance minimization subject to volume constraint for the single loading case. A dual formulation of this has been used for the multiple loading cases resulting in as many behavioral constraints as there are loading cases. The tentative topology given by the topology optimization module is taken and the domain boundary is approximated using straight lines, B‐splines and cubic spline curves and design variables are selected among the boundary defining points. Optimum boundary shape of the problem has been obtained using GA in two different ways: without stress constraints; and with stress constraints.

The proposed two stage strategy has been tested on benchmark structural optimization problems and its performance is found to be extremely good.

The strategy appears to be eminently suitable for implementation in a general purpose FE software as an add‐on module for structural design optimization.

It has been observed that the integrated topology and shape design method is robust and easy to implement in comparison with other techniques. The computing time requirements for the GA does not appear daunting in the present scenario of high performance parallel computing and improved GA techniques.

This paper shows how the evolutionary structural optimization (ESO) algorithm can be used to achieve a multiple criterion design for a structure in a thermal environment. The proposed thermal ESO procedure couples an evolutionary iterative process of a finite element heat conduction solution and a finite element thermoelastic solution. The overall efficiency of material usage is measured in terms of the combination of thermal stress levels and heat flux densities by using a combination strategy with weighting factors. The ESO method then works by eliminating from the structural domain under‐utilized material. In this paper, a practical design example of a printed circuit board substrate is presented to illustrate the capabilities of the ESO algorithm for thermal design optimization in multiple load environments.

The purpose of this paper is to provide an effective members-adding method for truss topology optimization in plastic design.

With the help of the distribution of principal stress trajectories, obtained by finite element analysis of the design domain, ineffective zones for force transmission paths can be found, namely, areas whose nodes may have ersatz nodal displacements. Members connected by these nodes are eliminated and the reduced ground structure is used for optimization. Adding members in short to long order and limiting the number of members properly with the most strained ones added, large-scale truss problems in one load case and multiple-load cases are optimized.

Inefficient members (i.e. bars that fulfil the adding criterion but make no contribution to the optimal structure) added to the ground structure in each iterative step are reduced. Fewer members are used for optimization than before; therefore, faster solution convergence and less computation time are achieved with the optimized result unchanged.

The proposed members-adding method in the paper can alleviate the phenomenon of ersatz nodal displacements, enhance computational efficiency and save calculating resources effectively.

In this paper a structural optimization technique based on a modified genetic algorithm (GA) is presented. The technique is developed to deal with discrete design optimization of structural steelwork. Also, the paper discusses the effect of different approaches, employed for the determination of the effective buckling length of a column, on the optimum design. In order to consider realistic steelwork design problems, a modified GA has been linked to a system of structural design rules (British Standards BS 5950 and BS 6399), interacting with a finite element package. In the formulation of the optimization problem, the objective function is the total weight of the structural members, as it gives a reasonably accurate estimation of the cost. The cross‐sectional properties of the structural members, which form the set of design variables, are chosen from two separate catalogues (universal beams and columns) covered by the British Standard BS 4. The minimum weight designs of two plane steel frame structures subjected to realistic multiple loading cases are obtained. These examples show that the modified GA in combination with structural design rules and more accurate analysis provides an efficient tool for practicing designers of steel frame structures. Finally, it is shown that the resulting design optimization is considerably influenced by a specific choice of a technique employed for the evaluation of the effective buckling length of structural members.

Most engineering products contain more than one component or structural element, a consideration that needs to be appreciated during the design process and beyond, to manufacturing, transportation, storage and maintenance. The allocation and design of component interconnections (such as bolts, rivets, or springs, spot‐welds, adhesives, others) usually play a crucial role in the design of the entire multi‐component system. This paper extends the evolutionary structural optimization method to the generic design problems of connection topology. The proposed approach consists of a simple cycle of a finite element analysis followed by a rule‐driven element removal process. To make the interconnection elements carry as close to uniform a load as possible, a “fully stressed” design criterion is adopted. To determine the presence and absence of the interconnection elements, the usage efficiencies of fastener elements are estimated in terms of their relative stress levels. This avoids the use of gradient‐based optimization algorithms and allows designers to readily seek an optimization of connection topology, which can be implemented in their familiar CAD/CAE design platforms. To demonstrate the capabilities of the proposed procedure, a number of design examples are presented in this paper.

Python codes are developed for the versatile structural analysis on a 3 spar multi-cell box beam by means of idealization approach.

Shear flow distribution, stiffener loads, location of shear center and location of geometric center are computed via numpy module. Data visualization is performed by using Matplotlib module.

Python scripts are developed for the structural analysis of multi-cell box beams in lieu of long hand solutions. In-house developed python codes are made available to be used with finite element analysis for verification purposes.

The use of python scripts for the structural analysis provides prompt visualization, especially once dimensional variations are concerned in the frame of aircraft structural design. The developed python scripts would serve as a practical tool that is widely applicable to various multi-cell wing boxes for stiffness purposes. This would be further extended to the structural integrity problems to cover the effect of gaps and/or cut-outs in shear flow distribution in box-beams.

In continuation of the recent development of Evolutionary Structural Optimisation (ESO) applied to the simultaneous objective to maximise the natural frequency and to minimise the mean compliance, presents the Multicriteria ESO optimisation of two new criteria. This has been done with the use of four different multicriteria methods. Three examples have been used to verify the usefulness and capability of these methods applied to ESO in the context of the aforementioned criteria. Concluded that the ESO weighting method is proficient in presenting the designer with a range of options (of Pareto attribute) taking into account multiple criteria, and the global criterion method has the tendency to produce shapes and topologies that resemble that of the weighted 50 per cent: 50 per cent method. Likewise, the logical OR operator method produced designs that corresponded directly to those of 100 per cent stiffness weighted criteria. No clear resemblance could be concluded with the case of the logical AND operator method.

The purpose of this paper is to describe a post‐processing procedure for defining load paths and a load bearing topology using the stresses from a finite element analysis.

Cauchy stress vectors and a Runge‐Kutta algorithm are used to identify the paths being followed by load components aligned with the coordinate axes. An algorithm is then defined which identifies an efficient topology that will carry the loads by straightening the paths.

The aim of the algorithm is to provide insight into the way a structure is carrying loads by identifying the material most effective in performing the load transfer. The procedure is applied to a number of structures to demonstrate its applicability to structural design.

The examples demonstrate an insight of structural behavior that is useful at the conceptual stage of the design process. The load paths identify load transfer and warn the designer of the creation of bending moments and the location of features such as holes on the load path. They also demonstrate that the new procedures can provide suggestions for alternate topologies for the load bearing structure.

The load path theory has been published elsewhere. The new work in this paper is the definition of the Runge‐Kutta algorithm to define the paths and the algorithm to identify the topology performing the load transfer.