Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 1: Finite strip formulation

This paper deals with the linear elastic analysis of prismatic folded plate and shell structures supported on diaphragms at two opposite edges with the other two edges arbitrarily restrained. The analysis is carried out using curved, variable thickness, Mindlin-Reissner finite strips. The theoretical formulation is presented for a family of C (0) strips and the accuracy and relative performance of the strips are examined for curved situations. Some variable thickness and elastically supported plates are considered and the interesting phenomenon of the occurence of boundary layers in the twisting moments and shear forces is highlighted for a common boundary condition. Other examples analysed include box girders and cylindrical shells. In all cases transverse shear deformation effects are included and the contributions to the strain energy from membrane, bending and transverse shear behaviour noted. In a companion paper these accurate and inexpensive finite strips are used for structural shape optimisation.     

Buckling optimization of variable thickness prismatic folded plates

This paper deals with the structural shape optimization of prismatic folded plates under buckling load consideration. Buckling loads are determined using linear, quadratic and cubic, variable thickness, C(0) continuity, Mindlin-Reissner finite strips. The whole structural optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, semi analytical sensitivity analysis and mathematical programming algorithm. The objective is either the maximization of the critical buckling load or minimization of the cross-section of the prismatic folded plate with constraints on the volume and buckling loads. Several examples are included to illustrate various features of the optimization algorithm, including plates and stiffened panels.     

Meshing and integrated optimisation for free-form reticulated shells

Presented herein is a study on the meshing and the integrated optimisation technique combined with configuration and mechanical behaviour for free-form reticulated shells. It focuses on the realisation of the practical layouts of meshes and improves the evaluation criteria for grid quality. For the preparation for the integrated optimisation, the bicubic quasi-uniform B-spline surface is applied to describe the free-form surface, and the energy method is introduced to smooth free-form reticulated shell through fairing factors. In order to perform optimisation automatically, a novel integrated optimisation system is established including fairing, finite element analysis (FEA) and optimisation programme modules. Based on the relationship between the fairing factors and the structural configuration, the zoned fairing factors are chosen as design variables (DVs). The FEA module is introduced to analyse and calculate the total structural strain energy of the structural components. By using the optimisation module, the optimum structural configuration can be found when the total structural strain energy reaches the minimum. Numerical results demonstrate that the proposed optimisation technique is convenient and feasible.     

广州歌剧院空间异型大跨度钢结构设计

广州歌剧院建筑造型奇特,其屋盖与幕墙组成的外围护体系为空间不规则折面组合型体,结构采用了空间折板式三向斜交单层网格结构。本文对其结构体系、构型和网格划分原则、杆件截面选取及节点形式等设计情况进行介绍,列举结构在重力荷载、风荷载、地震作用及温度作用下的变形和内力情况,对结构整体稳定分析、节点分析和铸钢节点足尺试验等关键问题进行论述,并对结构的工作机理和受力特性进行总结。结果表明,该体系对奇异建筑型体的适用性强,侧向刚度和抗震性能良好,结构工作机理以刚架作用为主,整体稳定问题不突出,结构对初始缺陷不敏感。     

Shape optimization method of free-form cable-braced grid shells based on the translational surfaces technique

Cable-braced grid shells, being a new type of single-layer reticulated shell, are widely used in glass roofs. However, research on the shape optimization of free-form cable-braced grid shells is relatively lacking. This paper describes a shape optimization method for cable-braced free-form grid shells, with strain energy used as the optimization object, structural height used as the optimization variable, and the conjugate gradient method used as the optimization algorithm. According to the shape forming method for grid shells, their shape optimization can be realized only by adjusting the generatrix and directrix, not by optimizing the whole surface. The B-spline curve method is used to model the generatrix and directrix and maintain an optimized surface fairing. The following conclusions can be drawn from this study. First, the structural mechanical behavior of grid shells can be significantly improved with rapid convergence using the proposed shape optimization method. Second, the plane quadrilateral mesh is maintained and fewer optimization variables are needed during the proposed shape optimization method. Finally, the optimized surface is fairing and the mechanical properties of the optimized surface are somewhat decreased when using the B-spline curve method.     

Experimental and finite element study of profiled steel sheet dry board folded plate structures

Folded plate structures constructed with profiled steel sheeting connected to dry boards by self drilling, self tapping screws (known as the PSSDB system) are being proposed as an alternative to traditional forms of roof construction. This paper describes the analysis, testing, and the structural behaviour of such kind of structures. The proposed efficient and load bearing structural system consists of an assembly of individual PSSDB panels connected by steel angle plates at the ridges, formed to the required shape, width and span. An analytical model using finite element method has been proposed. The profiled steel sheeting was idealised as an equivalent homogeneous orthotropic thin shell plate elements of constant thickness. Two directional plate elements were proposed in modelling the connection between profiled steel sheeting and dry board to include biaxial shear deformation. The proposed analytical method has been used to analyse the results of full-scale folded plate PSSDB tests and is found to give good results.     

板壳结构非线性屈曲分析的修正拉格朗日法

本文采用退化曲壳有限单元,推导了板壳结构非线性有限元分析的、修正的拉格朗日法(Updated Lagrauge简称U.L.法,下同),并编制了非线性有限元程序.利用本文理论方法既可分析板壳的太变形问题,同时也可考虑材料进入非线性后的太应变问题.通过对一些板壳屈曲问题的分析对比,证明了本文理论方法的正确性和有效性.     

Minimum weight of internally pressurised domes subject to plastic load failure

A series of eight mild steel domes subjected to internal pressure were tested up to burst in order to verify optimal solutions obtained by a zero order optimisation subroutine and a stress analysis code. Four classes of minimum weight domes were obtained. The first one was sought within torispherical shells of constant wall thickness. The second case corresponded to a variable meridional profile described by a generalised ellipse and a given wall thickness. In the third case, the uniform wall thickness became an additional design variable. In the fourth case both the meridional shape and variable wall thickness along the meridian were used as design variables. The plastic load was greater than 20 MPa in all four cases. The weight reduction obtained for the above mentioned four cases was 18, 19, 27 and 31%, respectively. Comparison with the fully stressed design is also provided.     

An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner–Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.     

Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes

The vibration of Mindlin plates with moving concentrated load is investigated using the finite element method (FEM). The use of Mindlin elements may, depending on the refinement of the mesh, yield poor results if the loads are located at off-nodal positions. A new strategy that is based on an adaptive mesh scheme and on the use of perturbation technique in the structural vibration simulation is proposed in this paper to overcome this problem. The strategy supports the use of the traditional finite elements and arbitrary geometry and boundary conditions for both plates and shells.     

拱型变厚度折板结构的内力分析

本提出一种新的空间结构,即圆拱型变厚度折板结构,并用有限单元板力学法对其进行内力分析。考虑折板的板厚变化,在两对边为弹性支承条件下,推导出板挠度的系列递推公式,从而获得折板间棱边的连接弯矩,进而求出每折板的内力。     

自由曲面结构形态创构方法——高度调整法的建立与其在工程设计中的应用

曲面结构(如壳体)的受力性能主要取决于结构的曲面形状。在实际工程中,常规的简单曲面一般较难有效满足结构的受力合理性。利用曲面高度参数与结构应变能之间的关系,提出了一种自由曲面创构方法来保证结构达到“薄”而“刚”的统一。该方法基于有限元法,通过计算应变能对曲面高度的微分,并根据应变能变化的敏感程度对曲面高度进行调整,最终得到一个结构应变能最小的合理结构形态。利用该方法,可以通过调整设计参数(约束条件,空间条件)得到多种合理曲面形态,供设计人员参考。同时,也可以对建筑意图所设定的初始形状进行修改,求得近似合理的结构几何形状。工程设计实例表明,该方法所得到的曲面结构基本以薄膜应力为主,而且能保证足够的刚度。     

The application of direct search optimisation to structural design

Development of an optimisation method suited to structural engineering design applications is described briefly. The method is essentially a conventional direct-search technique with exterior penalty constraints but uses variable penalty factors during the search to improve mobility between feasible regions. The method is illustrated by application to design of a composite box-girder footbridge, employing eight design variables and nineteen constraints, and the results are used to demonstrate the importance of considering sub-optima as well as the global optimum. The usefulness of univariant parameter/cost relationships in the region of global and local optimum points, derived as an intrinsic part of the optimisation process, is also stressed.     

Concurrent multi-scale modelling and updating of long-span bridges using a multi-objective optimisation technique

This paper aims at developing an innovative technique of concurrent multi-objective optimisation for updating the multi-scale model of long-span bridges. A multi-scale model is established for the purpose of concurrently analysing the global response of the structure and nonlinear local damages in order to assess structural state and local damage evolution or deteriorating, respectively. A multi-objective optimisation technique is proposed in this work for concurrent multi-scale model updating, in which several key issues including the determination of the objective functions and constraint conditions, the multi-objective optimisation algorithm and how to find the optimal solution from many non-inferior solutions are studied. The proposed concurrent multi-objective optimisation technique is applied to update the initial multi-scale model of Runyang Suspension Bridge (RYSB) near Shanghai, and the updated model is validated by the data from the field tests conducted for obtaining the response in global (dynamic properties) and local levels.     

Analytical solution for forced vibration of a simply-supported V-shaped folded plate roof

In this paper, the equation of the middle surface of a simply-supported V-shaped folded plate roof is established by means of step function. Then the forced vibration response of a simply-supported V-shaped folded plate roof is obtained by using the vibration theory of plates and shells and Navier's method. After that, the frequency equation of free vibration of a simply-supported V-shaped folded plate roof is given. Finally, a numerical illustrative example of this roof is presented. From the comparison of the results of this paper and the finite element results, the agreement is seen to be very good. This example also indicates that this analytical solution converges absolutely.     

Bending analysis of folded plates by the FSDT meshless method

In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results.     

Tragverhalten axial belasteter Stutzen in Kreiszylinderschalen unter Berücksichtigung geometrischer und werkstofflicher Nichtlinearitäten

Axially loaded nozzles in circular cylindrical shells with geometric and physical nonlinearity. The load‐displacement‐relations and the ultimate loads of axially loaded nozzles in circular cylindrical shells are determined by FE‐analyses. These investigations take into account the bi‐linear stress strain behaviour of structural steels and large displacements and instabilities as well. The results which apply for 400 < R/t < 5000 and take into account steel grades up to S690 are presented in graphical form. It is assumed that the thickness t_r of the nozzle is not less than the thickness t of the cylindrical shell. A design rule is given for optimizing the dimensions of pads and insert plates with regard to the effect of the axial load on the nozzle.     

An efficient method for structural damage detection using a differential evolution algorithm-based optimisation approach

An efficient method employing the differential evolution algorithm (DEA) as an optimisation solver is presented here to identify the multiple damage cases of structural systems. Natural frequency changes of a structure are considered as a criterion for damage occurrence. The structural damage detection problem is first transformed into a standard optimisation problem dealing with continuous variables, and then the DEA is utilised to solve the optimisation problem for finding the site and extent of structural damage. In order to assess the performance of the proposed method for structural damage identification, some illustrative examples are numerically tested, considering also measurement noise. All the numerical results demonstrate the effectiveness of the proposed method for accurately determining the site and extent of multiple-structural damage. Also, the performance of the DEA for damage detection compared to the standard particle swarm optimisation is confirmed by a test example.     

Design optimisation for a low energy home in Sydney

A simple model for a detached house in Sydney is optimised using a building energy simulation program to reduce the annual heating and cooling requirement to the point where a heating and cooling system is no longer necessary. A net present cost analysis, including the construction cost, the HVAC capital cost, and the electricity cost for space heating and cooling, is used to conduct the optimisation. The insulation thickness of the walls and roof, the window type, the thickness of an internal thermal mass wall, and the night ventilation air change rate were varied in the optimisation. Results for the best performing optimisation cases are presented and compared with the net present cost for a similar house, designed to meet the BASIX energy efficiency requirement for New South Wales. The best performing optimisation cases are shown to have a lower net present cost than the equivalent BASIX compliant house. With a view towards creating an operationally zero energy house, an optimisation case with a very low space energy requirement is selected and a photovoltaic system is sized to cover the remaining household electricity consumption over the course of a year.     

网壳结构"折叠展开式"计算机同步控制整体提升施工技术

网壳结构“折叠展开式”计算机同步控制整体提升施工技术是一种新型的、技术先进的大跨度网壳结构的施工方法。它的基本思想是将网壳结构局部抽掉少量杆件,将结构分成若干区域,并设置一定数量的可动铰节点,使结构变成一个机构。在靠近地面拼装,然后采用液压提升设备,通过计算机同步控制,将结构提升到设计高度,再补充缺省杆件,使机构变成稳定的结构状态。这种方法可以节省大量脚手架,避免高空作业,保证施工人员的安全,适合矢跨比比较大的网壳结构,具有明显的经济效益和社会效益。网壳结构“折叠展开式”计算机同步控制提升施工技术由浙江大学空间结构研究中心提出,并在河南省鸭河口电厂108米跨度干煤棚网壳工程施工中得到首次应用。本文详细介绍“折叠展开式”整体提升施工技术的基本思想、施工工艺、节点构造、提升过程中结构受力特性、技术措施及其施工控制要求。