Comparison of classical Winter's bracing requirements of compressed truss chord with stability analysis of 3D truss-model

Most code requirements concerning bracing are based on principles developed by Winter. The present research is devoted to study a lateral buckling of truss with linear elastic side supports. The classical Winter's model of truss chord in the case of out of the truss plane buckling is compared with nonlinear analysis of 3D truss model. Full bracing condition, that permits the truss chord to support load level corresponding to an unbraced length equal to the distance between braces is calculated. Then an approximate buckling load with less than full bracing is developed and the model is modified to account for unequal normal force distribution in compressed chord. The coefficient of buckling length related to side support distance in function of bracing stiffness is also calculated. The results are compared to design code requirements. It is shown that buckling length of truss chord with side supports considered as elastic elements is larger than assumed in design codes. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computer simulation of a twisted nanotube buckling

We develop procedures for solving the problems of dynamic nanostructure deformation and buckling numerically. The procedures are based on discretization with respect to time of the nonlinear equations of molecular mechanics whose matrices and vectors are determined using the Morse potential for the central forces of interaction between atoms and fictitious truss elements accounting for the variations of the angle between atomic bonds. To determine the critical values of deformation parameters and the shapes of buckling nanostructures we use a stability loss criterion for solutions to nonlinear ordinary differential equations on a finite time interval. We implemented our procedures in the PIONER code, using which we solve the problem of a twisted nanotube buckling in the conditions of a quasistatic deformation. To determine the postcritical equilibrium modes we solve the same problem in a dynamic formulation. We show that the modes of equilibrium configurations of the nanotube in the initial postcritical deformation correspond to a buckling mode obtained both at the bifurcation point of quasistatic solutions and at the quasibifurcation point of dynamic solutions.     

Design of planar articulated mechanisms using branch and bound

This paper considers an optimization model and a solution method for the design of two-dimensional mechanical mechanisms. The mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously. The underlying mechanical analysis model is based on a truss representation allowing for large displacements. For mechanisms undergoing large displacements elastic stability is of major concern. We derive conditions, modeled by nonlinear matrix inequalities, which guarantee that a stable equilibrium is found and that buckling is prevented. The feasible set of the design problem is described by nonlinear differentiable and non-differentiable constraints as well as nonlinear matrix inequalities.To solve the mechanism design problem a branch and bound method based on convex relaxations is developed. To guarantee convergence of the method, two different types of convex relaxations are derived. The relaxations are strengthened by adding valid inequalities to the feasible set and by solving bound contraction sub-problems. Encouraging computational results indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality.     

An analytical spectral stiffness method for buckling of rectangular plates on Winkler foundation subject to general boundary conditions

An analytical spectral stiffness method is proposed for the efficient and accurate buckling analysis of rectangular plates on Winkler foundation subject to general boundary conditions (BCs). The method combines the advantages of superposition method, stiffness-based method and the Wittrick–Williams algorithm. First, exact general solutions of the governing differential equation (GDE) of plate buckling considering both elastic foundation and biaxial loading is derived by using a modified Fourier series. The superposition of such general solutions satisfy the GDE exactly and BCs approximately, which guarantees the rapid convergence and high accuracy. Then, based on the exact general solution, the spectral stiffness matrix which relates the coefficients of plate generalized displacement BCs and force BCs is symbolically developed. As a result, arbitrary BCs can be prescribed straightforwardly in the stiffness-based model. As an efficient and reliable solution technique, the Wittrick–Williams algorithm with the J₀ problem resolved is applied to obtain the critical buckling solutions. The accuracy and efficiency of the method are verified by comparing with other methods. Benchmark buckling solutions are provided for plates with all possible boundary conditions. Also, dependence of various factors such as foundation stiffness, load combinations and aspect ratio on the buckling behaviors are investigated.     

Influence of various design parameters on the quality of optimal shape design in topology optimization analysis

The paper presents the discrete structural topology optimization problem. The analysis was made for the formulation of optimal design with a compliance minimization (as the objective functional) of statically loaded continuum structures with constraints forced on mass of the structure. Two different algorithms were compared (one taken from the literature and the second originally prepared) in order to study influence of design parameters formulation on the calculations results. Optimal topologies were presented and discussed for several 2D examples, with various optimization process parameters in order to get the best results in the shortest possible time. Other goal of presented research is to find out the possibilities of applying proposed algorithm in the designing process of bridge girders. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal layout of cantilever trusses

For given allowable stress, Michell (Ref. 1) has investigated the optimal design of a cantilever truss that is to transmit a given load to two given fixed points of support. Disregarding the weight of the connections between the bars, he found that the truss of minimum weight is a truss-like continuum with an infinity of joints, and with bars that are mostly of infinitesimal length. In the present paper, a finite number of joints is enforced by including in the structural weight, which is to be minimized, not only the weight of the bars but also the weight of their connections, which is assumed to be proportional to the number of joints. The concept of two adjoint trusses is introduced, each of which coincides with the Maxwell diagram of the other truss. Two adjoint trusses have the same weight, and an optimal truss is therefore self-adjoint. The optimal configurations of 6-joint and 11-joint cantilever trusses are discussed, and the range of the weight of the typical joint is determined for which the 6-joint truss is optimal.     

Instability analysis of space trusses using exact tangent-stiffness matrices

A simple (exact) expression for the tangent-stiffness matrix of a space truss undergoing arbitrarily large deformation, as well as member buckling, is given. An arc-length method is used to solve the tangent-stiffness equations in the post-buckling range of the structural deformation. Several examples to illustrate the viability of the present approaches in analyzing large space structures, simply, efficiently, and accurately, are given.     

A practical fractional numerical optimization method for designing economically and environmentally friendly super-tall buildings

Due to the complexity of super tall buildings, many well-known optimization algorithms are not well applicable. Using structural lateral system of super tall buildings as engineering background, the paper developed a practical fractional numerical optimization method (FNOM), which applies fractional strategy and quasi-constant assumption, to reduce material cost and embodied carbon cost by searching the optimal structural dimensions. Firstly, two kinds of relationships among optimization variables (structural dimensions), driven design constraints (the interstory drift and the natural period) and optimization objective (cost including material cost and embodied carbon cost) are mathematically modelled. Genetic algorithm (GA) is then introduced to search the optimal structural dimensions based on the quasi-constant assumption of virtual work and internal work of the inactive components. Thirdly, fractional strategy is applied to create assemblies composed of different structural component sets, and the assemblies are then to be optimized in proper sequences. Fourthly, FNOM is implemented as a user-friendly software called C-FNO to practically support the preliminary design of super-tall buildings. Finally, a 700 m high super-tall building is employed to illustrate FNOM by using C-FNO, and the results show that only three design constraints of the interstory drift, the natural period and the stress ratio need to be solved during each optimization step. Belt truss, mega column, outrigger truss and shear wall of the super tall building should be optimized in sequence to save more cost. A great amount of cost can be still saved for the super tall building with the normal traditional design.     

Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very time-consuming. This paper presents an alternative formulation, semidefinite programming with complementarity constraints, and proposes an efficient heuristic. The proposed method is based upon the concave–convex procedure for difference-of-convex programming. It is shown that the method can often find a practically reasonable truss design within the computational cost of solving some dozen of convex optimization subproblems.     

A new multi-objective discrete robust optimization algorithm for engineering design

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.     

基于绳索作动器的大型太空望远镜桁架结构的振动主动控制

薄膜衍射是一种新型的太空望远镜的成像方式,它具有轻质、易折叠与展开、光学成像精度高等许多优点,是当今太空望远镜技术的研究热点.该文针对一类薄膜衍射太空望远镜桁架结构的振动主动控制进行了研究,提出了一种基于绳索作动器的振动主动控制策略.首先建立了望远镜桁架结构的动力学模型,然后采用粒子群优化算法研究了绳索作动器的优化布置...     

An efficient algorithm for the regular W<Subscript>1</Subscript> packing of polygons in the infinite plane

This paper describes a new algorithm, PLANEPACK, which determines an optimal or near optimal solution for the W₁ packing of identical shapes in the infinite plane. Restricted to polygons for computational convenience, it is based on the no-fit polygon/configuration space obstacle approach. The algorithm was tested on a modest set of fourteen polygons (thirteen non-interlocking and one interlocking) and yielded a feasible solution for each. The solutions were optimal for four of the non-interlocking polygons and near optimal for the other nine. As expected though, the solution for the one interlocking polygon was sub-optimal and enhancements to the algorithm would be required for such cases.     

Synchronous/Asynchronous Buckling of Double-Layered Microplate Systems北大核心CSCD

采用修正的偶应力理论和双变量高阶剪切变形理论,发展了层间填充弹性介质的双层微板系统在面内压缩荷载作用下的屈曲模型.基于Euler-Lagrange方程推导了系统屈曲的控制微分方程,运用Navier法获得了上下层均为四边简支时系统同步/异步屈曲的解析解.通过数值算例讨论了系统各参数对其屈曲特性的影响.结果表明：系统的异步屈曲特性依赖于材料尺度参数、长宽比和弹性介质模量,而同步屈曲特性仅依赖于前两项,并且异步屈曲荷载高于同步屈曲荷载;弹性介质的Pasternak模量较之于Winkler模量对系统的屈曲特性影响更显著.     

Optimal sensor placement for spatial lattice structure based on three-dimensional redundancy elimination model

Spatial lattice structures are widely applied in engineering fields attributed to their superiorities in weight and reasonable stress. It is essential to select the best sensor placement layout for structural health monitoring and safety purposes, yet it is neither realistic nor efficient to place sensors in every location possible on the structure. To meet the strong requirements for optimal sensor placement in spatial lattice structure, this paper aims to investigate a combined objective function based on effective independence method and three dimensional redundancy elimination model to balance between optimal sensor placement performance and elimination in redundancy. To eliminate redundant information and resource waste caused by the clustered sensor distribution, the three-dimensional redundancy elimination model is constructed with the consideration of nearer nodes and overall sensor distribution ranges in three-dimensional cases. In addition, the combined function is constructed by giving the two component functions equal significance using weighting factors and normalization, and solved by genetic algorithm. Finally, the proposed method for spatial lattice structure is supported by three numerical examples including a simple lattice structure, a ground spatial truss structure and a space docking modular in space solar power satellite.     

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

In this paper, a recently proposed global Lipschitz optimization algorithm Pareto-Lipschitzian Optimization with Reduced-set (PLOR) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIviding RECTangles (DIRECT), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems.     

Application of the sequential parametric convex approximation method to the design of robust trusses

We study an algorithm recently proposed, which is called sequential parametric approximation method, that finds the solution of a differentiable nonconvex optimization problem by solving a sequence of differentiable convex approximations from the original one. We show as well the global convergence of this method under weaker assumptions than those made in the literature. The optimization method is applied to the design of robust truss structures. The optimal structure of the model considered minimizes the total amount of material under mechanical equilibrium, displacements and stress constraints. Finally, Robust designs are found by considering load perturbations.     

2D frames optimization. Criterion: maximum stability

Structural analysis was one of the first disciplines to demand powerful computing tools. However, with current capacities of both calculus and manufacture and use of new materials, along with certain aesthetic conditions, it is possible to address problems such as the one presented in this article, whose aim is the optimal variation of any frame, so that few criteria are met, including stability. The problem is complex and must be solved numerically. This paper presents a formulation for solving the optimization problem, considering not only the buckling conditions but any other, such as allowable stress or limited displacement. The equilibrium of each beam in its deformed geometry is proposed under assumption of small displacements and deformations (Second Order Theory). The optimization problem is mathematically formulated to determine which values maximize the buckling load of the frame and numerically solved by sequential quadratic programming. Finally, for the optimal solution from the point of view of stability, the plastic collapse load is calculated. The plastic behavior is based on the bending moment and leads to sudden concentrated plastic hinges. Therefore, the structural stability is affected, which is checked during the loading process.     

气体钻井钻柱轴扭耦合动态屈曲数学建模与求解

针对钻柱轴扭耦合动态屈曲的基本问题构造哈密顿体系,在辛几何空间中将临界屈曲载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛几何算法.方法较好的解决了钻柱轴扭耦合动态屈曲的复杂边界条件问题.在解决气体钻井钻柱动态屈曲问题的研究中具有良好的应用前景.     

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.