Variable Stiffness Design Research Articles

A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization

The advantages of laminated composite structures make them attractive in industrial applications. To achieve the maximum advantages of the composite structures, the design optimization is of great importance. This paper classifies and compares various optimization problems and methods in laminated composite structure design. Three kinds of problems are illustrated in this paper: constant stiffness design, variable stiffness design, and topology optimization. The main optimization methods used in laminated composite structure design, including the gradient-based methods, heuristic methods, and hybrid methods, are presented. The advantages and shortcomings of each method are discussed in detail. Finally, constant and variable stiffness design and topology optimization of laminated composite structures which have been solved in literature are reviewed.

Algorithmic Design of Low-Power Variable-Stiffness Mechanisms

Compliant actuators enabling low-power stiffness adaptation are missing ingredients and key enablers of next generation robotic systems. One of the key components of these actuators is the mechanism implementing stiffness adaptation that requires sophisticated control and nontrivial mechanical design. However, despite recent advances in controlling these systems, their design remains experience based and not well understood. In this paper, we present an optimization-based computational framework for the design of intrinsically low-power compliant variable stiffness mechanisms. The core ingredient of this framework is the mathematical formulation of the design problem—provided by a constrained nonlinear parameter optimization—which is computationally solved here to identify optimal variable stiffness designs. We show the basic capability of this formulation in finding parameters for variable stiffness mechanisms that require the least power by design. Further, we demonstrate the generality of this method in cross-comparing mechanisms with different kinematic topology to identify the one that requires the least power by design.

Optimal design of variable stiffness laminated composite truncated cones under lateral external pressure

The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure (FPF) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness (PS) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load.

Fast cylinder variable-stiffness design by using Kriging-based hybrid aggressive space mapping method

In this study, a surrogate assisted hybrid aggressive space mapping method is suggested to optimize buckling loads of cylinder variable stiffness composites made by fiber steering. Compared with other popular space mapping algorithms, both of surrogate and coarse FE model are integrated to obtain the coarse FE model-based solution. Moreover, the accuracy of surrogate can be enhanced by the sample points evaluated by the fine FE model. Therefore, the suggested method is easy to converge. After optimization by using the suggested algorithm, the buckling load of the variable stiffness cylinder optimized by the method has 43.12% improvement than the constant stiffness cylinder and 32.12% improvement than the quasi-isotropic cylinder, respectively. Therefore, it suggests that the suggested method has potential capability to handle complicated design for composites and can be extended to other complicated disciplines.

Optimal lay-up design of variable stiffness laminated composite plates by a layer-wise optimization technique

ABSTRACTThe optimal lay-up design for the maximum fundamental frequency of variable stiffness laminated composite plates is investigated using a layer-wise optimization technique. The design variables are two fibre orientation angles per ply. Thin plate theory is used in conjunction with a p-element to calculate the fundamental frequencies of symmetrically and antisymmetrically laminated composite plates. Comparisons with existing optimal solutions for constant stiffness symmetrically laminated composite plates show excellent agreement. It is observed that the maximum fundamental frequency can be increased considerably using variable stiffness design as compared to constant stiffness design. In addition, optimal lay-ups for the maximum fundamental frequency of variable stiffness symmetrically and antisymmetrically laminated composite plates with different aspect ratios and various combinations of free, simply supported and clamped edge conditions are presented. These should prove a useful benchmark for optimal lay-ups of variable stiffness laminated composite plates.

Review of the mechanical performance of variable stiffness design fiber-reinforced composites

Abstract Variable stiffness design (VSD) has been paid more attention for its capability of further exploiting the potential of fiber-reinforced composite in composite structure design. VSD under different mechanical property indexes is reviewed in this paper. The review mostly focuses on strength, buckling, frequency, and other more common mechanical indices. Subsequently, the usage of VSD method for several years is briefly summarized. Some successful tests about variable stiffness composite parts are introduced and the experiment results are also addressed. The article summarizes the research situation from both perspectives based on a number of papers about the VSD of composite materials in recent years and provides theoretical reference and basic knowledge to new researchers.

M902 内反足に対する可変剛性短下肢装具の構造設計に関する研究(GS2 バイオエンジニアリング(1),修士研究発表セッション)

M902 内反足に対する可変剛性短下肢装具の構造設計に関する研究(GS2 バイオエンジニアリング(1),修士研究発表セッション)

Design and Manufacturing of Variable Angle Tow Laminate

Variable angle tow (VAT) laminates have shown enhanced stiffness/strength performance compared to conventional straight fiber laminates. Employment of VAT allows utilizing variable stiffness design of composite structure, thus it widens the design possibilities. As a result, composite structure with improved mechanical characteristics can be manufactured. The main aims of the current study are to give an overview on methods and algorithms used for analysis and design of VAT laminates, and to develop technology and equipment for manufacturing laminate with improved structural performance. In order to improve the accuracy of the compaction process, a set of experiments were carried out using a simple testing device. For measuring the compaction force, a pneumatic cylinder, pressure regulator and digital manometer were used. The temperature of the consolidation area and the heat distribution were screened with the thermal camera. Infrared heater was used as a heating source. Material used in the experiment was carbon fiber reinforced polyamide.Findings show that in addition to the main parameters – the compaction force and temperature, there are many minor factors, such as the compaction wheel diameter, material and surface roughness of the compaction roller, the material and surface roughness of the mold and the pretension in the laminating tape and also the laminating speed, all influence the quality of the final product.Key words: Advanced Fiber Placement Technology, Automated Fiber Placement, Automated Tape Laying, Fiber Reinforced Composites, Laminates

Analysis of semi-active vehicle suspension system using airspring and MR damper

With the new advancements in vibration control strategies and controllable actuator manufacturing, semi-active actuators and dampers are finding their way as an essential part of vibration isolators, particularly in vehicle suspension systems. This is attributed to the fact that in a semi-active system, the damping coefficients can be adjusted to improve ride comfort and road handling performances. The currently available semi-active damper technology uses MR fluid to control the damping characteristics of the suspension system. In addition to MR dampers, combining air springs in a semi-active suspension system leads to better handling and ride performance in vehicles. Furthermore, the use of air spring in semi-active suspension system helps to ease design of variable spring stiffness. This easy design opportunity leads to independent control of stiffness and ride height of the vehicle. This paper deals with the design and modelling of variable stiffness air spring for semi-active suspension system, modelling of semi-active suspension systems with variable stiffness and MR damper, and study their

Micro-Spring’s Variable Stiffness Design and Characteristics Analysis

The variable stiffness micro-springs’ load and deformation have nonlinear relationship, thus they can be used in special occasions. MEMS processing technology can manufacture any complex structures in a plane, using this feature, a variable stiffness design idea for the planar micro-spring is proposed. That is, using one type of structure named contact pairs to achieve stiffness change during the micro-spring’s stretching process. Using contact pairs, two types of variable stiffness springs are designed: stiffness increase spring and stiffness convexity spring. Because of the influence of processing precision, the contact pairs’ sizes of the first type of variable stiffness spring are different each other, the machining error makes the test results and simulation results various. In order to avoid the above problem of above spring, this paper designs another two variable stiffness micro-springs, test results indicate that the improved variable stiffness springs can realize the variable stiffness’ tendency.

Defect layer method to capture effect of gaps and overlaps in variable stiffness laminates made by Automated Fiber Placement

A variable stiffness design can increase the structural performance of composite laminates. In this paper, a composite laminate with curvilinear fiber paths is designed to maximize simultaneously its in-plane stiffness and buckling load. After obtaining the Pareto front through a surrogate-based optimization algorithm, two variable stiffness laminates among the solution set are selected that can be manufactured by an Automated Fiber Placement machine. Due to the characteristics of the manufacturing process, defects appearing in the form of gaps and/or overlaps emerge within the composite laminate. MATLAB subroutines are developed here to capture the location and extent of the defects. A novel method, called defect layer, is proposed to characterize the change in properties of each layer in the composite laminates that results from the occurrence of gaps and overlaps. Such a method allows calculating the in-plane stiffness and buckling load of a composite laminate with embedded defects. The results show that by incorporating gaps in the laminates the buckling load improvement resulting from fiber steering reduces by 15% compared to the laminates where gaps are ignored. A maximum improvement of 71% in the buckling load over the quasi-isotropic laminates can be observed for a variable stiffness laminate built with a complete overlap strategy.

Surrogate-based multi-objective optimization of a composite laminate with curvilinear fibers

A variable stiffness design can increase the structural performance of a composite plate and provides flexibility for trade-offs between structural properties. In this paper, we examine the simultaneous optimization of stiffness and buckling load of a composite laminate plate with curvilinear fiber paths. The problem, which falls in the area of multi-objective optimization, is formulated and solved through a surrogate-based optimization algorithm capable of finding the set of optimum Pareto solutions. We integrate surrogate modeling into an evolutionary algorithm to reduce the high computational cost required to solve the optimization process. The results show that a curvilinear fiber path can increase both buckling load and stiffness simultaneously over the quasi-isotropic laminate. Furthermore, the optimum direction for varying the fiber angle is dependent on the loading direction and boundary conditions. The results for a plate under uniform compression with free transverse edges shows that varying the fiber orientation perpendicular to the loading direction can increase the buckling load by 116% with respect to that of a quasi-isotropic laminate.

A Variable Stiffness Method Application to Tunnel Support

This paper focuses on finding a more effective bolting design method. Stress and displacement of variable stiffness beam were calculated by using material mechanics, variable stiffness bolting designs was simulated using FLAC5.0 software. The calculation indicates that the maximum displacement of a variable stiffness beam is less than that in a constant stiffness beam, while same material quantity is used; and proper variable stiffness designs can improve the bolting effect while same total quantity of bolts is used according to the simulations.

A Variable Stiffness Method Application to Tunnel Support

This paper focuses on finding a more effective bolting design method. Stress and displacement of variable stiffness beam were calculated by using material mechanics, variable stiffness bolting designs was simulated using FLAC5.0 software. The calculation indicates that the maximum displacement of a variable stiffness beam is less than that in a constant stiffness beam, while same material quantity is used; and proper variable stiffness designs can improve the bolting effect while same total quantity of bolts is used according to the simulations.

Design of variable stiffness panels for maximum strength using lamination parameters

Tailoring of laminated composite structures by changing ply angle and thickness locally provides a unique opportunity to take full advantage of anisotropic properties of composite materials. Variable stiffness design has become more attractive with the development of industrial fibre placement machines. Strength design is one of the areas where fibre steering is advantageous. Design methods that consist of directly optimising fibre angles or fibre path coefficients can lead to local optima and/or non-continuous solutions. These problems can be alleviated by using lamination parameters as design variables, which provide a compact definition of laminate stiffness. Additionally these parameters are continuous and the design space has shown to be convex. Dependency of strength failure criteria on ply angles may preclude using lamination parameters as design variables. Here, a recently developed method which incorporates the strength failure criteria in the lamination parameter space by using a conservative failure envelope for all ply angles is utilised. A hybrid approximation for the failure index is developed and is guaranteed to be convex using a convexifying approach. As an example strength maximisation of a panel with a central hole under uniaxial tension is investigated. Numerical results show improvements in strength with respect to the quasi-isotropic design. Although there is a common belief that design for stiffness can be served as a surrogate for strength design, it is shown that considering the strength as a design criteria especially for structures with large stress gradients is very important.

Optimum stacking sequence design of composite materials Part II: Variable stiffness design

A composite laminate may be designed as a permutation of several straight-fiber layers or as a matrix embracing fibers positioned in curvilinear paths. The former called a constant stiffness design and the latter known as variable stiffness design. The optimization algorithms used in constant stiffness design were studied in Part I of this review article. This paper completes the previous article by focusing on variable stiffness design of composite laminates. Different parameterization and optimization algorithms are briefly explained and compared and the advantages and shortcomings of each algorithm are discussed.

Optimization of Variable-Stiffness Panels for Maximum Buckling Load Using Lamination Parameters

With the large-scale adoption of advanced fiber placement technology in industry, it has become possible to fully exploit the anisotropy of composite materials through the use of fiber steering. By steering the composite fibers in curvilinear paths, spatial variation of stiffness can be induced resulting in beneficial load and stiffness distribution patterns. One especially relevant area in which fiber steering has proved its effectiveness is in improving buckling loads of composite panels. Previous research used predefined forms of fiber angle variations and the coefficients of these analytic expressions were used as design variables. Alternatively, the local ply angles were used as design variables directly. In this paper, a framework is developed to treat the most general approach that considers the largest possible design space. The use of lamination parameters efficiently defines stiffness variation over a structural domain with the minimum number of variables. A conservative reciprocal approximation scheme is introduced. The inverse buckling factor is expanded linearly in terms of the in-plane stiffness and in terms of the inverse bending stiffness. The new approximation scheme is convex in lamination parameter space. Numerical results demonstrate improvements in excess of 100% in buckling loads of variable-stiffness panels compared to the optimum constant stiffness designs. Buckling load improvements are attributed primarily to in-plane load redistribution, which is confirmed both by the prebuckling stress distribution as well as by comparing the performance of designs optimized with variation of both in-plane and bending stiffness to those optimized with only bending stiffness variation. A tradeoff study between in-plane stiffness and buckling performance is also presented and shows the benefits of variable-stiffness design in enlarging the design possibilities of composite panels.

Optimum stacking sequence design of composite materials Part I: Constant stiffness design

Designing an optimized composite laminate requires finding the minimum number of layers, and the best fiber orientation and thickness for each layer. To date, several optimization methods have been introduced to solve this challenging problem, which is often non-linear, non-convex, multimodal, and multidimensional, and might be expressed by both discrete and continuous variables. These optimization techniques can be studied in two parts: constant stiffness design and variable stiffness designs. This paper concentrates on the first part, which deals with composite laminates with uniform stacking sequence through their entire structure. The main optimization methods in this class are described, their characteristic features are contrasted, and the potential areas requiring more investigation are highlighted.

607 荷重スイッチによる可変剛性を有する連続体構造設計(OS-2 構造設計)

607 荷重スイッチによる可変剛性を有する連続体構造設計(OS-2 構造設計)

Design of variable-stiffness composite panels for maximum buckling load

A generalized reciprocal approximation is presented for design of variable-stiffness laminated composite panels for maximum buckling load. The buckling load is expanded in terms of the inverse of the stiffness tensor. For discretized panels such an approximation has the important property of being separable, which allows the maximization to be carried out at each discrete node separate from the others. This makes the algorithm particularly suited to parallel computations. The sensitivity analysis is performed exactly using an adjoint method, requiring only one back substitution using the already factored inplane stiffness matrix with different right hand sides to compute the sensitivities for all design variables. A conforming CLPT finite element is used for the buckling analysis of rectangular plates and the proposed reciprocal approximation is used to update fiber orientation angles at each finite element node. Numerical results obtained for rectangular plates show that significant improvements can be gained in the buckling load by allowing the stiffness properties to vary spatially. The case of repeated eigenvalues is handled using a dual formulation.