Decomposition in Optimum Structural Design

To achieve the optimal feasible force density vector of a given geometry configuration tensegrity grid structure, an efficient procedure is presented for optimal initial self-stress design of tensegrity grid structures by consecutively solving two linear homogeneous systems in conjunction with a minimization problem. The nonlinear constrained optimization algorithm, known as the Interior-Point Method (I-PM), is utilized to obtain the minimal solution, leading to a set of force densities which guarantee the non-degeneracy condition of the force density matrix. The evaluation of the eigenvalues of tangent stiffness matrix is also introduced to check the geometric stability of the tensegrity grid structures. Finally, three numerical examples have been investigated comprehensively to prove the capability of the proposed method in optimal initial self-stress design of tensegrities. Furthermore, division of number of member group has been discussed in detail for the purpose of demonstrating the efficiency of the proposed method in seeking initial force densities of tensegrity grid structures.

On the Optimal Design of Structures in Vibrating State : 1st Report, A General Method of Optimal Design

This paper presents an optimization method for optimal engineering structure design. An interface procedure is essentially developed to combine the intelligent optimization algorithm and computer aided engineering (CAE) code. An optimization example is carried out to minimize the interlaminar normal stress of a laminate which affect the delamination failure of a laminate via arranging the stacking sequence. The analytical solution is calculated to validate the accuracy of optimization results.

The optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading is of great concern in the structural design of building structures. The research started around 1980 and many investigations have been conducted. A comprehensive review on this subject is made in this article. After the description of essential features of the optimal design problem of nonlinear building structures under earthquake ground motions, analysis types of optimization problems are explained and the significance of the dynamic pushover analysis is discussed from the viewpoint of analysis of limit states under earthquake ground motions of magnitude larger than the code-specified level. Then, the categorization by the response of frames and dampers was made. In this categorization, several subjects are discussed first: 1) Optimal design of bare nonlinear building frames under seismic loading, 2) Optimal design of nonlinear dampers for elastic building frames under seismic loading, 3) Optimal design of linear dampers for nonlinear building frames under seismic loading, 4) Optimal design of nonlinear building frames with specified nonlinear dampers under seismic loading, 5) Optimal design of nonlinear dampers for specified nonlinear building frames under seismic loading, 6) Simultaneous optimization of elastic-plastic building structures and passive dampers. Finally, the classification of researches in view of solution strategies is conducted for providing another viewpoint.

<p>This paper defines basic operations of neutrosophic numbers and neutrosophic number functions for objective functions and constraints in optimization models. Then, we propose a general neutrosophic number optimization model for the optimal design of truss structures. The application and effectiveness of the neutrosophic number optimization method are demonstrated through the design example of a two-bar truss structure under indeterminate environment to achieve the minimum weight objective under stress and stability constraints. The comparison of the neutrosophic number optimal design method with traditional optimal design methods proves the usability and suitability of the presented neutrosophic number optimization design method under an indeterminate / neutrosophic number environment.</p>

This paper is concerned with the numerical implementation of the boundary element method for shape optimal design of two-dimensional linear elastic structures. The design objective is to minimize the structural compliance, subject to an area constraint. Sensitivities of objective and constraint functions, derived by means of Lagrangean approach and the material derivative concept with an adjoint variable technique, are computed through analytical expressions that arise from optimality conditions. The boundary element method, used for the discretization of the state problem, applies the stress boundary integral equation for collocation on the design boundary and the displacement boundary integral equation for collocation on other boundaries. The use of the stress boundary integral equation, discretized with discontinuous quadratic elements, allows an efficient and accurate computation of stresses on the design boundary. This discretization strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally in the stress boundary integral equation, but also circumvents the problem of collocation at kinks and corners. The perturbation field is described with linear continuous elements, in which the position of each node is defined by a design variable. Continuity along the design boundary is assured by forcing the end points of each discontinuous boundary element to be coincident with a design node. The optimization problem is solved by the modified method of feasible directions available in the program ADS. Examples of a plate with a hole are analyzed with the present method, for different loading conditions. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of shape optimal design of structures.

Design of optimum structures

Chapter 1 Introduction of swarm intelligent algorithms.- Chapter 2 Application of particle swarm optimization algorithm to engineering structures.- Chapter 3 Optimum design of structures with heuristic particle swarm optimization algorithm .-Chapter 4 Optimum design of structures with group search optimizer algorithm .-Chapter 5 Improvements and applications of group search optimizer in structural optimal design .-Chapter 6 Optimum design of structures with quick group search optimization algorithm .-Chapter 7 Group search optimizer and its applications on multi-objective structural optimal design .-Chapter 8 Prospecting swarm intelligent algorithms.

In order to save project investment and reduce project quantity, the optimal design of aqueduct is the main problem in the project therefore, carrying out the optimal design and simulation analysis of U-shaped thin-walled aqueduct has important engineering application value. The paper takes Sha River aqueduct as the research object and adopts the direct search and point checking method of mixed discrete variable optimisation design. It also adopts the structural optimisation design method based on genetic algorithm and gives the optimal design scheme of U-shaped aqueduct. The optimisation design method has the advantages of fast convergence speed, high convergence efficiency and strong global search ability. The results show that, U-shape aqueduct structure is smooth, it has good mechanical properties, and the structural stress is small and can meet the strength requirement. The maximum vertical displacement of the aqueduct occurs in the middle of the span, the vertical displacement value is small, which can meet the requirement of stiffness.

LLC resonant converters are used in renewable energy applications to achieve high power efficiency conversions between different energy sources, buses, and energy storage elements. The traditional design methods for LLC resonant converters are based on the simple frequency domain analysis (FDA). However, the accuracy of FDA is not satisfactory, especially at wide voltage range applications. Considering the flexible power control requirements for photovoltaic systems, a wide voltage range operation is desired for the DC/DC converter. To overcome the drawbacks of traditional FDA method in wide range applications, the time domain analysis is adopted to achieve accurate analysis of LLC converters in this paper. Efficiency is normally selected as the optimization objective, where the circuit components and an accurate power loss model are required beforehand. To achieve a more general optimal design method for LLC converters, a simple root-mean-square (RMS) current and time domain analysis based optimal design method is proposed. The optimal design is achieved by minimizing the converter RMS current and ensuring some key design considerations. Moreover, an automated design tool for the proposed method is developed. Finally, a 2.5 kW experimental prototype is built with the estimated optimal circuit parameters. Experimental results under different operating conditions are demonstrated and the results are consistent with the theoretical analysis.

In this chapter, the optimum design problem of steel space frames is formulated according to the provisions of LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Corporation). The weight of the steel frame is taken as the objective function to be minimized. The design optimization problem necessitates selection of steel sections for the members of the steel frame from the available steel profiles lists. This turns the design optimization problem into discrete programming problem. Obtaining the optimum solution of such programming problems is cumbersome with mathematical programming techniques. On the other hand with the use of recently developed metaheuristic techniques that are based on swarm intelligence, the solution of the same problem becomes straightforward. Five different structural optimization algorithms are developed which are based on ant colony optimization, particle swarm optimizer, artificial bee colony algorithm, firefly algorithm, and cuckoo search algorithm, respectively. Two real size steel space frames; one rigidly connected and the other pin jointed are designed using each of these algorithms. The optimum designs obtained by these techniques are compared and performance of each version is evaluated. It is noticed that most of swarm intelligence-based algorithms are simple and robust techniques that determine the optimum solution of structural design optimization problems efficiently without requiring much of a mathematical struggle.

This paper includes description of reliability based design optimization of elasto-plastic skeletal structures under multi-parameter static loading. Presented approach is based on the assumption that the complementary strain energy of the residual forces is considered as an overall measure of the plastic performance for plastic shakedown analysis and optimal design of the structure, and this measure is an uncertain quantity responsible for resistance of the structure by assuming Gaussian distribution. The problems yield to nonlinear mathematical programming which are solved by the use of bi-level sequential quadratic algorithm. Simple portal frames are optimized to illustrate the proposed approaches.

Multi-objective optimization design of pile-anchor structures for slopes based on reliability theory considering the spatial variability of soil properties

The paper presents a simple yet efficient optimal design method based evolutionary structural optimization (ESO) to determine the minimum member sizes complying with an AISC-LRFD (an acronym for American Institute of Steel Construction – Load and Resistance Factor Design) specification. The influences of nonlinear (second-order approximation) geometry are realistically incorporated using an AISC 2010 direct analysis method. The optimization minimizes the total weight of structures subjected to the challenges associated with the simultaneous presence of nonlinear design formulations and discrete design variables realistically considering the availability of standard steel sections. This leads to a non-convex and/or non-smooth optimization program. The ESO algorithm overcomes the problem by performing iterative elimination procedures of ineffective sections, where the feasible design domain progressively converges to the minimum distribution of steel members satisfying limit state (ultimate strength and serviceability) criteria. The ESO design process is encoded within a visual basis application (VBA) framework having a direct interface with the commercial analysis and design software, called SAP2000. An illustrative example motivated by practical engineering applications has been successfully proceeded and hence highlighted robustness of the proposed approach in obtaining the optimal design of steel structures under applied forces.

The growing urgency for sustainable construction practices has necessitated a reevaluation of traditional design approaches in favor of more environmentally responsible methodologies. This paper presents a comparative analysis between optimal and adequate structural design within the context of sustainable construction. Focusing on two case studies—a cutting-edge, sustainably designed commercial building (the Bullitt Center) and a conventional mid-rise residential building in Chicago—the research explores how different design philosophies impact material efficiency, environmental footprint, economic performance, and occupant satisfaction.Through detailed life cycle assessments (LCA) and life cycle energy analyses (LCEA), the study quantifies the advantages of optimal design, which integrates advanced materials, renewable energy systems, and water conservation technologies. The findings demonstrate that while optimal design requires a higher initial investment, it significantly reduces long-term operational costs and environmental impact, achieving a net-zero energy status and greatly improving occupant well-being. In contrast, the conventional building, which adheres to standard design practices, exhibits higher embodied energy, greater environmental degradation, and lower occupant satisfaction.The paper concludes that optimal structural design is not only more sustainable but also economically viable over the building's life span. It emphasizes the importance of integrating sustainability from the earliest stages of design to achieve meaningful environmental and economic benefits. The study calls for the adoption of policy incentives and advanced modeling tools to facilitate the widespread implementation of optimal design principles in the construction industry. Keywords: Sustainable Construction, Optimal Structural Design, Adequate Design, Building Performance, Embodied Energy, Environmental Impact, Economic Viability, Material Efficiency