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.     

Optimal laminate design subject to single membrane loads

In this paper we investigate optimization of laminates for maximal membrane stiffness under single in-plane loads. The design parameters are the relative ply thicknesses and fiber orientations of an arbitrary number of plies. The design is allowed to vary in a pointwise fashion throughout the structure.From prior work on lamination parameters (Hammeret al. 1997), it is known that the optimal design is given by either some sort of two ply lay-up in special strain situations or otherwise by just a single rotated ply. This is exploited in the present analysis to derive analytically the unique parameters of the optimal design (cross-ply, angle-ply or single ply) as expressions of the membrane forces. Both high and low shear stiffness material are treated. Furthermore the analysis covers all possible local strain or membrane force situations.Finally, it is shown how these expressions for the optimal configuration of the laminate also appear as bounds on the principal membrane forces in order to obtain alignment between the numerically largest principal membrane force and principal strain.     

Optimal design of rigid-plastic beams subjected to dynamical loading

In the present paper the optimization problem of dynamically loaded simply supported beams is handled. The concept of a rigid-plastic body is used. The shape of the beam is sought, for which the integral residual deflection for a given time-instant and load is minimal. Two numerical methods for solving the problem are proposed. The numerical results are compared with those obtained by Lepik (1982).     

Reliability-based design optimization applied to structures submitted to random fatigue loads

Structural and Multidisciplinary Optimization - The reliability-based design optimization (RBDO) aims to find the most balanced design through a compromise between cost and safety when...     

Optimal design of shells against buckling subjected to combined loadings

In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by overall bending moment, constant or varying along an axis of a shell, by the appropriate shearing force and by an axial force and a constant torsional moment. We look for the shape of middle surface as well as the thickness of a shell, which ensures the maximum critical value of the loading parameter. The volume of material and the capacity of a shell are considered as equality constraints. The concept of a shell of uniform stability is applied.     

Optimal fastener pattern design considering bearing loads

In many engineering structures, failure occurs either at the connection itself or in the component at the point of attachment of the connection. To extend the service life of the structure it is important to ensure that the loads borne by the connections are distributed as uniformly as possible. This would also minimize the possibility of localized high stress regions within the component. In this work a topology optimization based approach has been developed to incorporate fastener load constraints into a problem formulated for optimal location of fasteners. The computational results indicate that it is effective in reducing the maximum fastener loads without compromising on the overall stiffness of the structure.     

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.     

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Presented at WCSMO-2, held in Zakopane, Poland, 1997     

Optimal design of adaptive structures Part II. Adaptation to impact loads

This paper is a continuation of the article entitled “Remodeling for Impact Reception.” It presents a generalization of the previously discussed concept on optimal remodeling of elasto-plastic structures exposed to impact load, where remodeling process is simulated via virtual distortion method (VDM). The resultant stiffest structure determined in the first part of this paper determines the initial configuration to design the optimal adaptive structure. It is assumed that considered structure can be equipped with so-called structural fuses with plastic-like behavior and controllable yield stress levels. Such an adaptive structure can still be optimized by the proper selection of locations for structural fuses and by the proper tuning of yield stress levels to the identified impact load. Maximization of the impact energy dissipation as the objective function allows significant reduction of residual vibrations after a few milliseconds. VDM-based algorithms for fast, complex reanalysis of dynamically loaded elasto-plastic structures and their sensitivity analysis are the key tools for the above-mentioned optimization procedures.     

Optimal shape design of functionally graded thickness inversion tubes subjected to oblique loading

This paper aims to understand and optimize the crush response of Functionally Graded Thickness (FGT) tubes with various thickness distributions subjected to oblique loading using multi-objective optimization method. Hence, finite element (FE) models are established and their results are validated by experimental tests. Two objective functions (specific energy absorption and peak load) are approximated by four different multi-objective optimization models: the weighted average, multi-design optimization (MDO) technique, constrained single-objective optimization, and geometrical average methods. The optimum design results demonstrate that the selection of appropriate inversion tube parameters such as the die radius, the coefficient of friction between the die and tube, and thickness distribution function have significant roles in the crashworthiness design. The results give new ideas to improve the crashworthiness performance of inversion tubes under oblique loading conditions.     

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.     

On optimization of interference fit assembly

This review presents developed models, theory, and numerical methods for structural optimization of trusses with discrete design variables in the period 1968 – 2014. The comprehensive reference list collects, for the first time, the articles in the field presenting deterministic optimization methods and meta heuristics. The field has experienced a shift in focus from deterministic methods to meta heuristics, i.e. stochastic search methods. Based on the reported numerical results it is however not possible to conclude that this shift has improved the competences to solve application relevant problems. This, and other, observations lead to a set of recommended research tasks and objectives to bring the field forward. The development of a publicly available benchmark library is urgently needed to support development and assessment of existing and new heuristics and methods. Combined with this effort, it is recommended that the field begins to use modern methods such as performance profiles for fair and accurate comparison of optimization methods. Finally, theoretical results are rare in this field. This means that most recent methods and heuristics are not supported by mathematical theory. The field should therefore re-focus on theoretical issues such as problem analysis and convergence properties of new methods.     

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.     

Numerical modeling of masonry-infilled RC frames subjected to seismic loads

The behavior of masonry-infilled reinforced concrete frames under cyclic lateral loading is complicated because a number of different failure mechanisms can be induced by the frame-infill interaction, including brittle shear failures of the concrete columns and damage of the infill walls. In this study, nonlinear finite element models have been used to simulate the behavior of these structures. Diffused cracking and crushing in concrete and masonry are described by a smeared-crack continuum model, while dominant cracks as well as masonry mortar joints are modeled with a cohesive crack interface model. The interface model adopts an elasto-plastic formulation to describe the mixed-mode fracture of concrete and masonry. The model accounts for cyclic crack opening and closing, reversible shear dilatation, and joint compaction due to damage. The constitutive models have been validated with experimental data and successfully applied to the dynamic analysis of a three-story, two-bay, masonry-infilled, non-ductile, reinforced concrete frame tested on a shake table. The results have demonstrated the capabilities of the finite element method in capturing the nonlinear cyclic load–displacement response and failure mechanisms of the structure, and indicated the important contribution of infill walls to the seismic resistance of a non-ductile reinforced concrete frame.     

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.     

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 design of imperfect,anisotropic, ring-stiffened cylinders under combined loads

Development of an algorithm to perform the optimal sizing of buckling resistant, imperfect, anisotropic ringstiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. An axisymmetric, geometrically nonlinear prebuckling equilibrium configuration is assumed and both stress and stability constraints are considered. The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state.     

Optimal staged self-assembly of linear assemblies

Natural Computing - We analyze the complexity of building linear assemblies, sets of linear assemblies, and $${\mathcal{O}}(1)$$ -scale general shapes in the staged tile assembly model. For systems...