Design Of Thin-walled Structures Research Articles

Incompatible Deformations in Hyperelastic Plates

The design of thin-walled structures is commonly based on the solutions of linear boundary-value problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among the substantial non-linear effects that significantly change the deformation properties of thin plates are the effects of residual stresses caused by the incompatibility of deformations, which inevitably arise during the manufacture of ultrathin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of this paper. To this end, the local unloading hypothesis is used. This makes it possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from the least action principle and variational symmetries taking account of the implant field. The derivations are carried out in the framework of elasticity theory for simple materials and, in addition, within Cosserat’s theory of a two-dimensional continuum. As illustrative examples, the distributions of incompatible deformations in a circular plate are considered.

An equivalent anisotropy orientation tensor algorithm for integrated material-structure design

This study presents the Equivalent Anisotropy Orientation Tensor (EAOT) algorithm as a novel approach for the integrated design of thin-walled structures composed of composite materials. The EAOT algorithm is designed to enhance the buckling load of structures by efficiently optimizing the distribution of strain energy density. In addition, the algorithm considers the fiber orientation and stiffener structure as orthogonal isotropic material, providing an innovative design methodology that surpasses conventional approaches. The EAOT algorithm incorporates a weighted function to account for the effects of different buckling modes, which solves the problem of mode overlap and exchange that affects the optimization effect. Utilizing the optimization results from the EAOT algorithm enables the realization of effective material-structure integrated design. Two case studies demonstrate the superior performance of designs based on this algorithm compared to conventional methods, resulting in a substantial increase in the critical buckling load by 15.3 % to 34.7 %.

Multi-objective optimization for snap-through response of spherical shell panels

Composite spherical shell panels are commonly used for the lightweight design of thin-walled structures in the structure, architecture, aerospace engineering. Depending on the shell panel length, thickness, curvature, and stacking sequence, the load-deflection response under lateral load can be either a completely stable equilibrium path or an unstable snap-through path. In this work, the response of simply supported cross-ply composite spherical shell panels subjected to lateral static loads is studied and optimized. The spherical shell exhibiting snap-through response is optimized to (a) maximize the load required to initiate snap-through and (b) minimize the unstable region. Meanwhile, the spherical shell exhibiting continuous response is optimized to (a) maximize the softening-hardening load and (b) minimize the shell weight. The decision variables for both constraint multi-objective optimization (CMOO) problems include layup sequence, thickness, and the radius of curvature to side length ratio. The nonlinear governing equations are derived based on Kirchhoff–Love hypotheses for thin shells and Hamilton's principle. A novel semi-analytical method is presented based on Bernstein polynomials combined with a fast iterative approach to compute the objective features of the responses. Benefiting from the high efficiency and robustness of the proposed approach, the CMOO problems are solved by the metaheuristic Multi-Objective Artificial Hummingbird Algorithm (MOAHA). Composite spherical shell panels with various geometry and lamination configurations are considered to validate the performance of the proposed method. The optimization of geometric parameters (shell curvature and thickness) in addition to the staking sequence provide a high degree of tailoring of the shell performance to meet various objectives. These parameters are taken as design variables that must be optimized to achieve some objectives and satisfy arbitrary nonlinear constraints.

Stability response assessment of steel thin-walled open-top tanks subjected to local support edge settlement

Purpose Vertical cylindrical welded steel tanks are typical thin-walled structures that are very susceptible to buckling under settlement. The major concern in the design of these thin-walled structures is buckling failure. On this basis and by considering the findings of the previously reported research works, the stability performance of open-top steel tanks with various industrial applications under local support edge settlement is further investigated in this paper. This study aims to contribute to the current state-of-the-art in the design and retrofit of such thin-walled structures. Design/methodology/approach The buckling behaviors of numerous cylindrical shell models with various height-to-radius, radius-to-thickness and settlement span ratios are investigated through linear and nonlinear buckling analyses. The effects of addition of a top stiffening ring on the buckling behavior of cylindrical steel tanks are studied as well. Findings This parametric study demonstrates that the choice of the height-to-radius, radius-to-thickness and settlement span ratios as well as addition of the top stiffening ring can be quite effective on the stiffness and strength performances, deformations and stress distribution as well as intensity of vertical cylindrical welded steel tanks subjected to local support edge settlement. Originality/value This research endeavor was formulated on the basis of a comprehensive literature survey and demonstrates the relationship between geometrical as well as stiffening features and buckling stability performance of open-top tanks subjected to local support edge settlement and also provides practical recommendations for design and retrofit purposes.

An active learning approach for multi-objective optimization and its application to the crashworthiness design of thin-walled structures

An active learning approach for multi-objective optimization and its application to the crashworthiness design of thin-walled structures

Design and Optimization of Negative Poisson Ratio Thin-Walled Tube Using Sensitivity-Based Response Surface Model Methodology

Under low-speed collision conditions, the thin-walled structures located at the forepart of passenger car act as a significant energy absorber, which can reduce the injury degree of passengers in collision accidents. Therefore, the design of thin-walled structures is particularly important in automobile body development. High stiffness and strength contribute to structural integrity, but the resulting large collision force will be detrimental to occupant safety. To address this issue, the paper proposed a novel negative Poisson ratio thin-walled tube (NPR-TWT). In addition, the second-order sensitivity-based response surface models (SB-RSMs) were established to improve the efficiency of design optimization. Furthermore, the NPR-TWT was optimized by using the non-dominated sorting genetic algorithm (NSGA-II) to enhance its comprehensive performance. The results showed that the optimized NPR-TWT could absorb collision energy by sufficient displacement deformation and reduce the peak impact force. It can provide theoretical and practical guidance for the application of thin-walled structures in automobile body safety.

Local buckling of omega-stringer-stiffened composite panels under compression–shear interaction

In the preliminary design of thin-walled structures the computational efficiency is especially important, as a high number of function evaluations of any computational analysis model is necessary. To further identify possible ways to reduce computational effort, the convergence behaviour and quality of different trial functions is investigated in the context of a computational model based on the Ritz-method. In the analysis framework, the local buckling behaviour of an omega-stringer-stiffened composite panel is investigated, where continuity conditions are ensured by the Lagrange multiplier method. The quality of the different trial functions assembled using trigonometric functions and Legendre polynomials is assessed in convergence and parametric studies.The load cases considered are uniaxial compression, biaxial compression, shear loading and their combinations. The most promising improvement on the results is identified by using a combination of a sine series and Legendre polynomials with simply supported boundary conditions.

Layout design of thin-walled structures with lattices and stiffeners using multi-material topology optimization

In this paper, the thin-walled structures with lattices and stiffeners manufactured by additive manufacturing are investigated. A design method based on the multi-material topology optimization is proposed for the simultaneous layout optimization of the lattices and stiffeners in thin-walled structures. First, the representative lattice units of the selected lattices are equivalent to the virtual homogeneous materials whose effective elastic matrixes are achieved by the energy-based homogenization method. Meanwhile, the stiffeners are modelled using the solid material. Subsequently, the multi-material topology optimization formulation is established for both the virtual homogeneous materials and solid material to minimize the structural compliance under mass constraint. Thus, the optimal layout of both the lattices and stiffeners could be simultaneously attained by the optimization procedure. Two applications, the aircraft panel structure and the equipment mounting plate, are dealt with to demonstrate the detailed design procedure and reveal the effect of the proposed method. According to numerical comparisons and experimental results, the thin-walled structures with lattices and stiffeners have significant advantages over the traditional stiffened thin-walled structures and lattice sandwich structures in terms of static, dynamic and anti-instability performance.

A novel nonlinear FE perturbation method and its application to stacking sequence optimization for snap-through response of cylindrical shell panel

Cylindrical shell panels are commonly used for the lightweight design of thin-walled structures in the aerospace engineering. In this work, the snap-through buckling of composite cylindrical shell panels subjected to lateral loads is calculated and designed. We present a novel method to extract the essential features of the snap-through response using a fast path-following scheme, and subsequently apply them as inputs to the stacking sequence optimization. In the path-following scheme, the full snap-through response can be achieved efficiently based on the finite element perturbation method, meanwhile its numerical accuracy is well guaranteed by the necessary corrections on residual forces. The essential features of the snap-through response, i.e. the load-limit point, critical deflection and jump deflection, are selected to be either the objective or the constraint in the stacking sequence optimization. The stacking sequence optimization using the genetic algorithm can be realized considering the severe geometrical nonlinearities of mechanics responses, benefiting from the high efficiency and robustness of a single function call. Composite cylindrical shell panels with various geometry/lamination configurations and load/displacement boundary conditions, are considered in the stacking sequence optimizations, to validate the good performance of the proposed method.

Microscopy imaging and modeling study on the mechanical properties of the primary flight feather shaft of the bean goose, Anser fabalis.

Avian flight feathers have the unique advantages of lightweight and high strength, which play a key role in their flight capacity. In this article, the rachis of the bean goose's primary flight feather was used as the research object. Its compressive properties were analyzed and the 3D microscale was observed by 3D microscope system with a super wide depth of field. The distribution of mechanical properties, section variation of fiber and internal microstructure of rachis were obtained by micro-CT technique. Based on these results, a 3D reconstructed model was established for structure mechanical simulation. The simulation results were close basically to the compressive strength of the actual sample. These results show that the synergistic effect of cortex and medulla can improve mechanical resistance of the rachis. Therefore, the best position (N3) of the primary flight feather shaft can be applied to the bionic design of thin wall structures for energy absorption. This research can provide some guidance for the application of lightweight structural design. RESEARCH HIGHLIGHTS: The internal structure of bean goose feather shaft was observed by micro-CT. The experimental method has a deeper understanding of the compressive properties of rachis fiber orientation. Under the synergistic effect of cortex and medulla, the compressive performance of rachis is better.

Topology optimization for maximizing linear buckling load based on level set method

Stability and buckling have attracted extensive attention in the design of structural elements, especially in the design of thin-walled structures since they may naturally have poor stability and be prone to buckling failure. This paper proposes a level-set based topology optimization (TO) method that can maximize the lowest linear buckling load under a mean compliance constraint. First, we conduct the linearized buckling analysis and formulate the optimum design problem. Second, we derive the design sensitivity and revisit the reaction-diffusion equation-based level-set topology optimization. Finally, we solve several two-dimensional benchmark problems and the design results are presented to validate the proposed method.

Crashworthiness Design and Multi-Objective Optimization for Bio-Inspired Hierarchical Thin-Walled Structures

Thin-walled structures have been used in many fields due to their superior mechanical properties. In this paper, two types of hierarchical multi-cell tubes, inspired by the self-similarity of Pinus sylvestris, are proposed to enhance structural energy absorption performance. The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load. The theoretical model of the mean crushing force is also derived based on the simplified super folded element theory. The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures. It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes. Furthermore, multi-objective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm, and the corresponding Pareto front diagram is obtained. This research provides a new idea for the crashworthiness design of thin-walled structures.

Finite strip method computer application for buckling analysis of thin-walled structures with arbitrary cross-sections

The Direct Strength Method (DSM) is a well-known formulation presented in the Brazilian standard ABNT NBR 14762:2010, that estimates the strength capacity of cold-formed steel (CFS) members. However, this formulation requires the elastic critical buckling loads as point of departure, regarding local (L), distortional (D) and global (G) modes, which can be obtained by (i) elastic buckling analysis or (ii) available direct equations. The present study is dedicated to the development of a computer program, FStr Computer Application, with graphical user interface (GUI), in order to make the buckling analysis easier and approachable for both research activities and engineering design of thin-walled structures with arbitrary cross-sections (sections combining closed cells with open branches). The proposed application uses the Finite Strip Method (FSM), mainly focused on a simple and accessible GUI, which was implemented in the MATLAB App Designer. Validation of the FStr was performed with the help of examples of open and closed cross-sections and comparison with the results of acknowledged computer programs, such as CUFSM and GBTul, based respectively on FSM and GBT (Generalized Beam Theory), as well as analytical procedures for the case of the global buckling modes. Both, the critical buckling loads expressed by the computed signature curve and the correspondent critical buckling modes are compared, confirming the adequate performance of the proposed computational tool. As future research, the authors plan updates for the FStr Computer Application, including the computation of the buckling modal participation and the automatic strength predictions, based on the DSM-based design prescriptions.

Multi-component topology optimization for thin-walled structures

This article presents a multi-component topology optimization method for thin-walled structures, which can be applied to two-dimensional plate components and three-dimensional tube components. Based on the theory of multi-component topology optimization for stamped sheet metal assemblies, an accurate calculation method for the Young’s modulus of joint elements is provided. To avoid the discontinuous derivative and improve the optimization efficiency, a non-zero gradient-based material interpolation scheme with penalization is constructed. The cost of die-set materials can be controlled effectively by the maximum size of components. Several topology designs based on minimized compliance confirm the effectiveness of the proposed method. The topology solutions illustrate that the proposed method can realize the structural design of thin-walled structures which can meet the die-set material cost requirement.

Out-of-plane crashworthiness of the new combined quasi-honeycomb core

As a type of cellular materials, honeycomb structures exhibit great advantages in mechanical properties and crashworthiness. This paper proposed a new kind of combined quasi-honeycomb core and studied on the out-of-plane crashworthiness. Research found that the new combined quasi-honeycomb have great advantages in energy absorption and crushing force efficiency than the conventional hexagonal and square honeycomb cores. Under the impact load of 10 m/s, specific energy absorption of quasi-honeycomb increased 37.8% and 66.2% than hexagonal and square honeycombs, and the crushing force efficiency respectively improved 47.6% and 63.2%. In this paper, a theoretical prediction model of the axial average crushing force for the quasi-honeycomb was established, and the structural parameters’ effect on crashworthiness were researched based on which. The contents in this paper are expected to provide some references for the crashworthiness optimal design of thin-walled structures.

Multi-scale optimisation of thin-walled structures by considering a global/local modelling approach

In this work, a design strategy for optimising thin-walled structures based on a global-local finite element (FE) modelling approach is presented. The preliminary design of thin-walled structures can be stated in the form of a constrained non-linear programming problem (CNLPP) involving requirements of different nature intervening at the different scales of the structure. The proposed multi-scale optimisation (MSO) strategy is characterised by two main features. Firstly, the CNLPP is formulated in the most general sense by including all design variables involved at each pertinent scale of the problem. Secondly, two scales (with the related design requirements) are considered: (a) the structure macroscopic scale, where low-fidelity FE models are used and (b) the structure mesoscopic scale (or component level), where more accurate FE models are involved. In particular, the mechanical responses of the structure are evaluated at both global and local scales, avoiding the use of approximated analytical methods. The MSO is here applied to the least-weight design of an aluminium fuselage barrel of a wide-body aircraft. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one, thanks to the implementation of a sub-modelling approach. The whole process is completely automated, and once set, it does not need any further user intervention.

Bionic design of thin-walled structure based on the geometry of the vascular bundles of bamboo

Several bamboo features are responsible for its known mechanical performance and thus were applied on bionic thin-walled structures, still the particular geometry of individual vascular bundles remains unexplored mechanically. This research investigates the mechanical influence of that region in the design of thin-walled structures, comparing it with bamboo-inspired designs from the literature. X-ray microtomography was used to explore bamboo bundle's geometry, applying it as reinforcement. The proposed new design showed improvements in strength and energy absorption in axial, lateral, and flexural explicit Finite Element Analyses. The vascular bundle's geometry was revealed as an important characteristic of bamboo performance.

Nonlinear bifurcation analysis of stiffener profiles via deflation techniques

When loading experiments are repeated on different samples, qualitatively different results can occur. This is due to factors such as geometric imperfections, load asymmetries, unevenly stressed regions or uneven material distributions created by manufacturing processes. This fact makes designing robust thin-walled structures difficult. One numerical strategy for exploring these different possible responses is to impose various initial imperfections on the geometry before loading, leading to different final solutions. However, this strategy is tedious, error-prone and gives an incomplete picture of the possible buckled configurations of the system. The present study demonstrates how a deflation strategy can be applied to obtain multiple solutions for the more robust design of thin-walled structures under displacement controlled uniaxial compression. We first demonstrate that distinct initial imperfections trigger different sequences of instability events in the Saint Venant–Kirchhoff hyperelastic model. We then employ deflation to investigate multiple bifurcation paths without the use of initial imperfections. A key advantage of this approach is that it can capture disconnected branches that cannot easily be discovered by conventional arc-length continuation and branch switching algorithms. Numerical experiments are given for three types of aircraft stiffener profiles. Our proposed technique is shown to be a powerful tool for exploring multiple disconnected bifurcation paths without requiring detailed insight for designing initial imperfections. We hypothesise that this technique will be very useful in the design process of robust thin-walled structures that must consider a variety of bifurcation paths.

Crashworthiness of innovative hexagonal honeycomb-like structures subjected to out-of-plane compression

Seeking for innovative structures with higher mechanical performance is a continuous target in railway vehicle crashworthiness design. In the present study, three types of hexagonal reinforced honeycomb-like structures were developed and analyzed subjected to out-of-plane compression, namely triangular honeycomb (TH), double honeycomb (DH) and full inside honeycomb (FH). Theoretical formulas of average force and specific energy absorption (SEA) were constructed based on the energy minimization principle. To validate, corresponding numerical simulations were carried out by explicit finite element method. Good agreement has been observed between them. The results show that all these honeycomb-like structures maintain the same collapsed stages as conventional honeycomb; cell reinforcement can significantly promote the performance, both in the average force and SEA; full inside honeycomb performs better than the general, triangular and double schemes in average force; meanwhile, its SEA is close to that of double scheme; toroidal surface can dissipate higher plastic energy, so more toroidal surfaces should be considered in design of thin-walled structure. These achievements pave a way for designing high-performance cellular energy absorption devices.

Crashworthiness topology optimization of thin-walled square tubes, using modified Bidirectional Evolutionary Structural Optimization approach

Abstract In this study, topology optimization of a thin-walled square tube subjected to an axial crushing load was carried out to enhance its crashworthiness performance, utilizing the modified Bidirectional Evolutionary Structural Optimization (BESO) procedure. In this way, by systematic searching, topology optimization finds the best material layout for the structure to satisfy the objective function. In each iteration, a new pattern of material-void through the tube walls can trigger various folding mechanisms. Thus, the energy absorption history trend might not be smooth and the ultimate pattern proposed by the algorithm is less likely to be the optimal one. With an emphasis on the BESO hypothesis regarding direct removal and addition of elements, the modified BESO algorithm excavated the optimal design in two steps. First, material-void patterns were produced, considering specific energy absorption as the element efficiency criterion. Then, the pattern with the least material usage which satisfies an energy absorption constraint was selected as the optimal design. Such an optimum layout also boosts the tube performance respecting peak crushing force, since the embedded voids through the structure serve as a crush initiator. The optimization code was developed in MATLAB, which was automatically integrated with ABAQUS software performing the nonlinear crushing analysis. To validate the finite element model, an experimental investigation was carried out on a simple square tube. Having performed the topology optimization and some fine-tuning process, the topologically optimized tube was constructed and experimentally tested. Results showed 16.21% weight reduction enriched with 36.57% enhancement in the peak crushing force by sacrificing less than 3.5% energy absorption, which represents substantial improvements from a crashworthiness viewpoint. The obtained interesting results showed the high potential of the BESO algorithm for the design of thin-walled structures under large deformation and out-of-plane buckling.