Efficient handling of stability problems in shell optimization by asymmetric ‘worst‐case’ shape imperfection

The paper presents an approach to shape optimization of proportionally loaded elastic shell structures under stability constraints. To reduce the stability‐related problems, a special technique is utilized, by which the response analysis is always terminated before the first critical point is reached. In this way, the optimization is always related to a precritical structural state. The necessary load‐carrying capability of the optimal structure is assured by extending the usual formulation of the optimization problem by a constraint on an estimated critical load factor. Since limit points are easier to handle, the possible presence of bifurcation points is avoided by introducing imperfection parameters. They are related to an asymmetric shape perturbation of the structure. During the optimization, the imperfection parameters are updated to get automatically the ‘worst‐case’ pattern and amplitude of the imperfection. Both, the imperfection parameters and the design variables are related to the structural shape via the design element technique. A gradient‐based optimizer is employed to solve the optimization problem. Three examples illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

An automatic optimization method for minimizing supporting structures in additive manufacturing

The amount of supporting structure usage has been a major research topic in layer-based additive manufacturing (AM) over the past years as it leads to increased fabrication time and decreased surface quality. Previous studies focused on deformation and topology optimization to eliminate the number of support structures. However, during the actual fabrication process, the properties of shape and topology are essential. Therefore, they should not be modified casually. In this study, we present an optimizer that reduces the number of supporting structures by identifying the prime printing direction. Without rotation, models are projected in each direction in space, and the basis units involved in the generation of support structures are separated. Furthermore, the area of the supporting structures is calculated. Eventually, the prime printing direction with minimal supporting area is obtained through pattern-searching method. The results of the experiment demonstrated that the printing area was reduced by up to 60% for some cases, and the surface quality was also improved correspondingly. Furthermore, both the material consumption and fabrication time were decreased in most cases. In future work, additional factors will be considered, such as the height of the supporting structures and the adhesion locations to improve the efficiency of this optimizer.The full text can be downloaded at https://link.springer.com/content/pdf/10.1007%2Fs40436-019-00277-y.pdf     

A bispace parameterization method for shape optimization of thin‐walled curved shell structures with openings

Simultaneous shape optimization of thin‐walled curved shell structures and involved hole boundaries is studied in this paper. A novel bispace parameterization method is proposed for the first time to define global and local shape design variables both in the Cartesian coordinate system and the intrinsic coordinate system. This method has the advantage of achieving a simultaneous optimization of the global shape of the shell surface and the local shape of the openings attached automatically on the former. Inherent problems, for example, the effective parameterization of shape design variables, mapping operation between two spaces, and sensitivity analysis with respect to both kinds of design variables are highlighted. A design procedure is given to show how both kinds of design variables are managed together and how the whole design flowchart is carried out with relevant formulations. Numerical examples are presented and the effects of both kinds of design variables upon the optimal solutions are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical solution of the Brazier problem for thin-wall pipes with initial cross-sectional shape imperfection in the case of action of pressure

An analytical method is proposed for the solution of geometrically nonlinear Brazier problem for thin-mall pipes with initial cross-sectional shape imperfection in the case of action of pressure. Geometrical equations relating displacement components to strains and equilibrium equations taking into account change in the curvature of pipe cross section and axis have been derived. A solution in a first approximation for dimensionless flexibility parameter is presented, the exactness of which is illustrated by numerous examples. For the case of joint action of external bending moment and pressure, a limit curve of the critical moment value as a function of pressure value has been obtained. __________ Translated from Problemy Prochnosti, No. 3, pp. 100–123, May–June, 2008.     

The universal scissor component: Optimization of a reconfigurable component for deployable scissor structures

Deployable scissor structures are well equipped for temporary and mobile applications since they are able to change their form and functionality. They are structural mechanisms that transform from a compact state to an expanded, fully deployed configuration. A barrier to the current design and reuse of scissor structures, however, is that they are traditionally designed for a single purpose. Alternatively, a universal scissor component (USC)—a generalized element which can achieve all traditional scissor types—introduces an opportunity for reuse in which the same component can be utilized for different configurations and spans. In this article, the USC is optimized for structural performance. First, an optimized length for the USC is determined based on a trade-off between component weight and structural performance (measured by deflections). Then, topology optimization, using the simulated annealing algorithm, is implemented to determine a minimum weight layout of beams within a single USC component.     

SHAPE OPTIMIZATION IN SHELL THEORY: Design Sensitivity of the Continuous Problem

We consider a non-shallow shell made of an isotropic homogeneous material, working in linear elastic conditions, subjected to a given load. Our aim is to change the shape of the shell so that it resists better towards a given criterion. By shape, we mean essentially the midsurface of the shell. The thickness could be added without any difficulty. The important aspect that we study here is the midsurface.

This problem is worked by gradient type methods. We prove that if the criterion depends on the displacement field through a differentiable function, then it depends on the shape in a differentiable manner, because the displacement field is a differentiable function of the shape. Then we present an analytical formula giving the exact gradient of the criteria before any discretization. After that, we explain how to compute numerically an approximation to this exact gradient. Then we give numerical results.     

Sensitivity analysis of frame structures (virtual distortion method approach)

A novel approach to sensitivity analysis of frame structures based on the virtual distortion method (VDM) has been presented. The sensitivity analysis has been performed for elasto‐plastic material behaviour with respect to selected structural parameters e.g. cross‐sectional area, hardening/softening coefficient and yield stress. Advantages of applying the virtual distortion method to sensitivity analysis have been emphasised i.e. making use of the so‐called influence matrix, constant for the whole analysis and solving only local sets of equations corresponding to plastic locations. Theoretical background as well as the whole variety of examples has been presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Sensitivity analysis of truss structures (virtual distortion method approach)

A new approach to structural sensitivity analysis based on the so-called virtual distortion method is presented. The proposed methodology enables the calculation of derivatives for elastic as well as elasto-plastic structures on the basis of knowledge of current strains, permanent plastic deformations and influence matrix, describing interactions between a chosen member and the entire structure. The analytical basis as well as numerical verification of the concept is demonstrated. Advantages of the proposed approach, in the sense of numerical cost, are summarized in conclusions. © 1998 John Wiley & Sons, Ltd.     

Stimulating Equivalent Geometric Imperfections for the Numerical Buckling Strength Verification of Axially Compressed Cylindrical Steel Shells

A geometrically and materially nonlinear analysis with imperfections included (GMNIA) is currently the most sophisticated and perspectively the most accurate method of a numerical buckling strength verification. By this way, equivalent geometric imperfections, which have to cover the influence of all deviations from the nominal data of the resistance parameters, are fundamental. The problem of consistent equivalent geometric imperfections includes the problems of their shape and size. It is recommended to start from the failure modes of the perfect structure in order to get imperfection patterns, which are unfavourable with respect to buckling resistance, relevant referring to manufacture and easy to use. The influence of the imperfection length is not sufficiently attended in the present design codes. It is proposed to use the full wave length of the ideal ring buckling mode as the imperfection length of the equivalent geometric imperfection for the basic buckling case of the axially compressed cylindrical shell. Finally, proposals are made for consistent equivalent geometric imperfection amplitudes of this buckling case.     

An alternative determination of unmodified temperature T1 for eliminating thermal strain during load testing of engineering structures

A method of determining the unmodified temperature, T₁, for elimination of thermal strain from the load testing is presented. It is based on the fact that the intersection point of two T–ε lines for a test point shows zero stress (or strain) and coincides with the known zero stress at the neutral axis of the structure, if the test point is set at the axis. The abscissa of this intersection point indicates the unmodified temperature T₁. The method has been applied to the load test on a suspect beam in a 4-storey building. The conclusion was reached that although the suspect beam was weaker than normal, it could take the assigned load without any remedial measures. This conclusion was verified by the practical evidence of normal service for more than five years.
The method is applicable to certain types of structures at the moment.     

Optimization of lifetime maintenance strategies for deteriorating structures considering probabilities of violating safety, condition, and cost thresholds

Modern maintenance strategies for deteriorating structures are typically based on minimizing total cost. Extensions of this concept into the nondeterministic range allow to take into account the uncertainty in total cost. In this paper, the probability of exceeding a total cost threshold is included in the structure maintenance optimization problem. In addition, the probabilities of violating acceptable levels of safety and condition are computed. Based on this, an optimization task can be formulated and solved in which these probabilities can be included into the formulation of the objective function and the constraint conditions. Smoothing of the Monte-Carlo-based results is carried out utilizing a smoothing procedure by regression methods which are well-known for the response surface approach.Both time-based maintenance and performance-based maintenance are taken into account. The total maintenance cost is minimized with respect to parameters of both types of maintenance. Taking into account the cost of failure, optimal values for the threshold safety level and the time interval between subsequent maintenance applications are obtained.It is shown that different design parameters can lead to the same total cost thus allowing for a trade-off between time-based maintenance and performance-based maintenance at the discretion of the structure maintenance manager.     

含孔复合材料点阵夹层结构数值计算方法及其影响因素

针对含孔复合材料点阵夹层结构在面内压缩载荷作用下的失效模式及其影响因素问题,通过实验对含孔复合材料点阵夹层结构失效模式进行了研究;基于3D Hashin准则和Chang-Chang刚度退化准则建立了含孔复合材料点阵夹层结构有限元渐进损伤失效分析模型,并将计算结果与实验结果进行了对比;基于有限元分析方法探讨了开孔形状、开孔率以及开孔位置对其极限承载力的影响。结果表明:当点阵夹层结构面板厚度较大时,含孔复合材料点阵夹层结构的主要失效模式为面板圧溃;通过对比有限元计算结果和实验结果,极限承载力的最大误差约为12%,失效位置与实验结果一致;当点阵夹层结构的对称面与载荷方向平行且孔的中心在对称面上时,面内压缩强度与开孔位置无关,主要受到开孔形状和开孔率的影响;当点阵夹层结构对称面与载荷方向垂直且孔的中心在对称面上时,边距大于一个胞元,面内压缩强度基本不变,边距小于一个胞元,面内压缩强度下降。     

Structural collapse analysis of framed structures under impact loads using ASI-Gauss finite element method

The main objective of this study is to devise a technique, which, when implemented into finite-element codes, is efficiently applicable to impact collapse analyses of framed structures. In this study, the formerly developed adaptively shifted integration (ASI) technique for the linear Timoshenko beam element is modified into the ASI-Gauss technique by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. On comparison with the ASI technique, the ASI-Gauss technique proves its higher accuracy and efficiency in elastic range. Moreover, instead of applying impact loads in the form of nodal forces, we consider the impact phenomenon by means of contacts between the elements involved and the elemental contact algorithm is verified from the point of conservation of energy. Impact analyses considering member fracture with different sets of parameters are performed using a high-rise framed structure and a small aircraft. From the results obtained, we can observe propagation phenomena of impact loads and shock waves. Also, a proper difference in impact damage is obtained by different sets of parameters. The results also indicate that the mass of the aircraft has a stronger influence on impact damage than its velocity. Moreover, soon after impact, tensile stresses are observed in the columns that were compressed by dead loads before impact.     

On the application of the probability transformation method for the analysis of discretized structures with uncertain proprieties

The aim of this work is to show a novel approach for the analysis of random systems. This approach, based on the application of the Probabilistic Transformation Method (PTM), is here developed for the study of uncertain structural systems. These systems are characterized by the fact that some of their geometrical and/or mechanical properties can be characterized only by a probabilistic point of view. In particular, the goal of the proposed approach is the evaluation of the probability density function (pdf) of a single response quantity avoiding the onerous operation of the variable saturation, which is necessary when the classical PTM is applied.     

Review of the mathematical background to the development of realistic load histories for fatigue testing relevant to tubular structures in the North Sea

Following the discovery of oil and gas, fixed welded tubular steel platforms were first installed in the North Sea in 1966. They are subjected to significant fatigue loads due to wave action. A report on proposed standard load histories was published in 1976. These were based on theoretical calculations. In 1979, increasing interest led to the formation of the Wave Action Standards History (WASH) Working Group. Strain gauge data for platforms in the North Sea were made available to the Working Group so later standard load histories were based on service data rather than theoretical calculations. Mathematical techniques used are reviewed, and some load histories are described as case studies. A framework was developed that could be used to formulate a particular standard load history but left open the option of incorporating alternative features, with relatively little additional work.     

Optimization of support positions to maximize the fundamental frequency of structures

In this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd.     

基于概率-凸集混合模型的汽车正面碰撞结构可靠性优化设计

本文基于概率和凸集模型研究汽车正面碰撞可靠性优化设计问题。根据汽车吸能结构厚度、材料参数等不确定参数类型,分别采用概率和多椭球凸模型进行描述,以汽车正面碰撞安全性可靠性指标为约束,考虑汽车吸能结构质量为优化目标,建立了一种基于混合模型的可靠性优化设计模型。采用拉丁方试验设计构造了目标函数和约束函数的Kriging近似模型,利用功能度量法求解可靠度指标值,通过基于移动因子序列优化与可靠性评定将嵌套优化解耦为单层次优化。实际算例表明算法具有较高的计算效率及精度,对实际设计工作有一定参考价值。     

A reduced SAND method for optimal design of non-linear structures

An SQP-based reduced Hessian method for simultaneous analysis and design (SAND) of non-linearly behaving structures is presented and compared with conventional nested analysis and design (NAND) methods. It is shown that it is possible to decompose the SAND formulation to take advantage of the particular structure of the problem at hand. The resulting reduced SAND method is of the same size as the conventional NAND method but it is computationally more efficient. The presentation here builds on previous research on SAND methods generalizing the solution approach to cases with both equality and inequality constraints. The new version of the reduced SAND method is tested in the context of weight minimization of 3-D truss structures with geometrically non-linear behaviour. © 1997 John Wiley & Sons, Ltd.     

A method of calculating deviations of the shape of cylindrical structures relative to the median cylinder

A method of calculating the deviations of the shape relative to the median cylinder for a uniform and nonuniform arrangement of monitored points along the perimeters of monitored sections is considered and an example of the use of the algorithm is presented. __________ Translated from Metrologiya, No. 6, pp. 27–31, 2007.