Complex-shaped beam element and graph-based optimization of compliant mechanisms

Compliant mechanisms are designed to be intentionally flexible, providing hingeless mechanisms. This work contributes a complex-shaped beam element formulation in conjunction with the ground structure approach. We identify compliant mechanism design solutions by using evolutionary topology optimization and increase flexibility by using a parametrization concept based on graph theory. The new operators for evolutionary optimization are also explained and sample problems are used to address the question of how our contribution increases design solutions space.     

Six-axis force sensor evaluation and a new type of optimal frame truss design for robotic applications

The different means currently available for six-axis wrist force sensor evaluation are discussed, and a unified criteria is proposed that is based on the condition number, the overall static and dynamic stiffness of the sensor, and the strain gauge sensitivity. In this light a new frame/truss type of sensor body design is introduced. The uniqueness of the design lies in the elastic members that exhibit truss (axial deformation), as opposed to the commonly used beam (bending) behavior. Several improvements over previous designs result, including: increased force sensitivity with a consistently low condition number, increased rigidity, and improved design flexibility. In addition, a design methodology is presented that uses optimization theory in combination with finite element analysis, to yield the best possible frame/truss force sensor design for a given set of specified principal forces.     

Concurrent topology optimization of multiscale structures with multiple porous materials under random field loading uncertainty

Aim of this work is the synthesis of auxetic structures using a topology optimization approach for micropolar (or Cosserat) materials. A distributed compliant mechanism design problem is formulated, adopting a SIMP–like model to approximate the constitutive parameters of 2D micropolar bodies. The robustness of the proposed approach is assessed through numerical examples concerning the optimal design of structures that can expand perpendicularly to an applied tensile stress. The influence of the material characteristic length on the optimal layouts is investigated. Depending on the inherent flexural stiffness of micropolar solids, truss–like solutions typical of Cauchy solids are replaced by curved beam–like material distributions. No homogenization technique is implemented, since the proposed design approach applies to elements made of microstructured material with prescribed properties and not to the material itself.     

Truss topology optimization considering local buckling constraints and restrictions on intersection and overlap of bar members

This paper illustrates the application of a two-level approximation method for truss topology optimization with local member buckling constraints and restrictions on member intersections and overlaps. Previously developed for truss topology optimization with stress and displacement constraints, that method is achieved by starting from an initial ground structure, and, combined with genetic algorithm (GA), it can handle both discrete and continuous variables, which denote the existence and cross-sectional areas of bar members respectively in the ground structure. In this work, this method is improved and extended to consider member buckling constraints and restrict intersection and overlap of members for truss topology optimization. The temporary deletion technique is adopted to temporarily remove buckling constraints when related bar members are deleted, and in order to avoid unstable designs, the validity check for truss topology configuration is conducted. By using GA to search in each possible design subset, the singularity encountered in buckling-constrained problems is remedied, and meanwhile, as the required structural analysis is replaced with explicit approximation functions in the process of executing GA, the computational cost is significantly saved. Moreover, for the consideration of restrictions on member intersecting and overlapping, the definition of such phenomena and mathematical expressions to recognize them are presented, and a new fitness function is developed to include such considerations. Numerical examples are presented to show the efficacy of the proposed techniques.     

考虑间隙运动副的桁架单胞等效建模与分析

本文主要研究了含间隙运动副桁架单胞的等效建模方法.主要考虑了桁架单胞的等效刚度问题以及阻尼问题.首先从间隙铰链开始研究,提出全面的铰链模型;其次提出用位移法将桁架单胞等效成板,即把桁架单胞看成是由梁元组成的钢架结构,运用平面钢架位移法得出桁架单胞的等效刚度矩阵,进而得出结构的整体固有频率和等效后的板的刚度矩阵.最后用有限元软件ANSYS对单胞结构在不同边界条件下进行了模态分析,将在自由边界条件下的固有频率和解析得出的频率做了对比,发现二者有很好的吻合度.结果表明由于间隙运动副的存在,使得桁架单胞结构的刚度降低,柔性增强.     

压电自适应桁架结构智能振动控制

介绍了采用模糊神经网络模型进行振动主动控制的压电自适应桁架结构设计、应用及实验结果. 设计了一种具有自适应结构技术的压电主动构件结构, 并提出了具有5层结构能够自调整隶属函数的模糊神经网络控制模型. 为了验证控制模型的有效性, 搭建了配置压电主动构件的双跨桁架结构试验平台, 通过检测误差信号, 由模糊神经网络控制模型确定主动构件的驱动输出. 试验结果证实了模糊神经网络控制模型在振动抑制方面的有效性.     

Large-scale framed structure as parallel mechanism with hyper-redundancy

The truss, a typical framed structure, is a fixed/dead structural system. A variable system is derived from the truss by installing a kinematic pair in each of the truss members. The system obtained is not a structure but a mechanism in the conventional sense. This is the truss-type mechanism, and it is hyper-redundant and quite flexible due to the highly multiple degrees of freedom when derived from the large scaled truss. The truss-type mechanism is used as a deployable structure and an adaptive structure. This article reviews the story of the evolution from the truss as a fixed structure to the adaptive truss structure. This system has a broad potential to create versatile flexibility in the structural system in general, although current applications are concentrated on space structure engineering.     

High-payload climbing and transitioning by compliant locomotion with magnetic adhesion

This paper presents a new climbing robotic mechanism for high-payload climbing and wall-to-wall transitioning. Payload capacity and transition ability are very important in climbing-robot applications for heavy industries and construction industries. The proposed robotic platform consists of three magnetic tread-wheel modules that are connected by links with two compliant joints. The front compliant joints are passive type with a torsion spring, and the rear compliant joints are active type with torque-controlled motors. A torque-controlled tail is attached at the end of the third module. Various transitions are achieved by the compliant joints, which change shape depending on the external conditions. High payloads are achieved by the large contact area of three magnetic tread-wheel modules. Detailed design issues are presented with analyses of the design parameters. The robot can perform two internal and two external transitions against gravity and every possible transition in the side surface driving direction. The robot can carry 10 kg payloads on vertical surfaces and on a ceiling. The ability to overcome a 30 mm diameter obstacle on vertical surfaces is also verified by experiments. The proposed robotic platform is going to be used in heavy industries.     

A new level set method for systematic design of hinge-free compliant mechanisms

This paper presents a new level set-based method to realize shape and topology optimization of hinge-free compliant mechanisms. A quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is employed to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. The design of compliant mechanisms is mathematically represented as a general non-linear programming with a new objective function augmented by the high-order energy term. The structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. In doing so, it is expected that numerical difficulties such as the Courant-Friedrichs-Lewy (CFL) condition and periodically applied re-initialization procedures in most conventional level set methods can be eliminated. In addition, new holes can be created inside the design domain. The final mechanism configurations consist of strip-like members suitable for generating distributed compliance, and solving the de-facto hinge problem in the design of compliant mechanisms. Two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms.     

Fuzzy finite element analysis of imprecisely defined structures with fuzzy nodal force

This paper presents the fuzzy finite element analysis for static displacements of fixed free stepped rectangular beam, truss and simplified bridge structure with fuzzy nodal force. The material and geometric properties of the structures are taken as crisp. Fuzzy finite element analysis of static problem for the above structures converts the problem into fuzzy system of linear equations. As such the coefficient matrix and the right-hand side vector become crisp and fuzzy respectively. A new approach is used here to solve the fuzzy system of linear equations. Numerical results for the three stepped rectangular beam, three-bar truss and simplified bridge with fifteen elements are presented to illustrate the computational aspects of the developed method. The results obtained are depicted in term of plots.     

A swift technique for damage detection of determinate truss structures

In this study, a novel two-stage approach for damage detection of determinate truss structures is proposed. The method lies in the group of vibration-based methods but it just needs the first natural frequency and mode shape vector of these structures for identifying the location and severity of damage. In the first stage, the modal residual force vector for different modes of a structure is introduced and the one associated with the first mode is applied to the structure as an external nodal force vector. Then, the residual local nodal force vector can be computed for all elements of the structure. Next, the elements with non-zero residual internal force are considered as damaged elements. In the second stage, the damage severity of each damaged element is determined using a new relation which can be categorized as a force–displacement relation. To show the efficiency and simplicity of the proposed method, three truss structures including a 13-bar planar truss, a 29-bar planar truss, and a 77-bar planar truss under different damage scenarios are studied; the results of which indicate that the method is innovatively capable of suitably detecting, for determinate truss structures, not only damaged members but also their individual damage severity by carrying solely one analysis.

     

Robust topology optimization accounting for misplacement of material

The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics during the optimization process. The proposed method is successfully applied to three example problems: the minimum compliance design of a slender column-like structure and a cantilever beam and a compliant mechanism design. An extensive Monte Carlo simulation is used to show that the obtained topologies are more robust with respect to geometric imperfections.     

Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme

Topology optimization of truss lattices, using the ground structure method, is a practical engineering tool that allows for improved structural designs. However, in general, the final topology consists of a large number of undesirable thin bars that may add artificial stiffness and degenerate the condition of the system of equations, sometimes even leading to an invalid structural system. Moreover, most work in this field has been restricted to linear material behavior, yet real materials generally display nonlinear behavior. To address these issues, we present an efficient filtering scheme, with reduced-order modeling, and demonstrate its application to two- and three-dimensional topology optimization of truss networks considering multiple load cases and nonlinear constitutive behavior. The proposed scheme accounts for proper load levels during the optimization process, yielding the displacement field without artificial stiffness by simply using the truss members that actually exist in the structure (spurious members are removed), and improving convergence performance. The nonlinear solution scheme is based on a Newton-Raphson approach with line search, which is essential for convergence. In addition, the use of reduced-order information significantly reduces the size of the structural and optimization problems within a few iterations, leading to drastically improved computational performance. For instance, the application of our method to a problem with approximately 1 million design variables shows that the proposed filter algorithm, while offering almost the same optimized structure, is more than 40 times faster than the standard ground structure method.     

Truss topology optimization including bar properties different for tension and compression

The problem of optimum truss topology design based on the ground structure approach is considered. It is known that any minimum weight truss design (computed subject to equilibrium of forces and stress constraints with the same yield stresses for tension and compression) is—up to a scaling—the same as a minimum compliance truss design (subject to static equilibrium and a weight constraint). This relation is generalized to the case when different properties of the bars for tension and for compression additionally are taken into account. This situation particularly covers the case when a structure is optimized which consists of rigid (heavy) elements for bars under compression, and of (light) elements which are hardly/not able to carry compression (e.g. ropes). Analogously to the case when tension and compression is handled equally, an equivalence is established and proved which relates minimum weight trusses to minimum compliance structures. It is shown how properties different for tension and compression pop up in a modified global stiffness matrix now depending on tension and compression. A numerical example is included which shows optimal truss designs for different scenarios, and which proves (once more) the big influence of bar properties (different for tension and for compression) on the optimal design.     

The stiffness spreading method for layout optimization of truss structures

A novel optimization method, stiffness spreading method (SSM), is proposed for layout optimization of truss structures. In this method, stiffness matrices of the bar elements in a truss structure are represented by a set of equivalent stiffness matrices which are embedded in a weak background mesh. When the proposed method is used, it is unnecessary for the bar elements in a truss structure to be connected to each other during the optimization process, and each of the bar elements can move independently in the design domain to form an optimized design. Another feature of the method is that the sensitivity analysis can be done analytically, making gradient based optimization algorithms applicable in the solution. This method realizes the size, shape and topology design optimization of truss structures simultaneously and allows for more flexibility in topology change. Numerical examples illustrate the feasibility and effectiveness of the proposed method.

     

Hybridizing electromagnetism-like mechanism algorithm with migration strategy for layout and size optimization of truss structures with frequency constraints

The optimal design of a truss structure with dynamic frequency constraints is a highly nonlinear optimization problem with several local optimums in its search space. In this type of structural optimization problems, the optimization methods should have a high capability to escape from the traps of the local optimums in the search space. This paper presents hybrid electromagnetism-like mechanism algorithm and migration strategy (EM–MS) for layout and size optimization of truss structures with multiple frequency constraints. The electromagnetism-like mechanism (EM) algorithm simulates the attraction and repulsion mechanism between the charged particles in the field of the electromagnetism to find optimal solutions, in which each particle is a solution candidate for the optimization problem. In the proposed EM–MS algorithm, two mechanisms are utilized to update the position of particles: modified EM algorithm and a new migration strategy. The modified EM algorithm is proposed to effectively guide the particles toward the region of the global optimum in the search space, and a new migration strategy is used to provide efficient exploitation between the particles. In order to test the performance of the proposed algorithm, this study utilizes five benchmark truss design examples with frequency constraints. The numerical results show that the EM–MS algorithm is an alternative and competitive optimizer for size and layout optimization of truss structures with frequency constraints.     

On the prediction of topology and local properties for optimal trussed structures

A new formulation is presented for mathematical modelling to predict the distribution of material, material properties, and topology for the optimal design of trussed structures. The design problem is cast in a form to minimize a measure ofgeneralized compliance, which is calculated as a sum over the structure of weighted displacement. Member stiffnesses appear as design variables and, starting with a given ground structure, the solution predicts the optimal layout and distribution of stiffness. The isoperimetric constraint in the reformulated problem measures totalcost in generalized form, based on independently specified unit relative cost factors for each truss element. One or another form of optimal design is generated via a process where designated elements in the unit relative cost field are adjusted systematically at each cycle. The generalized cost feature provides as well for the introduction of certain technical constraints into the design problem, e.g. the facility to design around obstacles. Results for each cycle of an algorithm for computational treatment are identified as the solution to a properly posed optimization problem. Computational procedures are demonstrated by the prediction of optimal designs for a variety of truss problems in 2D.     

Optimum design of geometrically nonlinear space trusses

A structural optimization algorithm is developed for geometrically nonlinear three-dimensional trusses subject to displacement, stress and cross-sectional area constraints. The method is obtained by coupling the nonlinear analysis technique with the optimality criteria approach. The nonlinear behaviour of the space truss which was required for the steps of optimality criteria method was obtained by using iterative linear analysis. In each iteration the geometric stiffness matrix is constructed for the deformed structure and compensating load vector is applied to the system in order to adjust the joint displacements. During nonlinear analysis, tension members are loaded up to yield stress and compression members are stressed until their critical limits. The overall loss of elastic stability is checked throughout the steps of algorithm. The member forces resulted at the end of nonlinear analysis are used to obtain the new values of design variables for the next cycle. Number of design examples are presented to demonstrate the application of the algorithm. It is shown that the consideration of nonlinear behaviour of the space trusses in their optimum design makes it possible to achieve further reduction in the overall weight. The other advantage of the algorithm is that it takes into account the realistic behaviour of the structure, without which an optimum design might lead to erroneous result. This is noticed in one of the design example where a tension member changed into a compression one at the end of nonlinear analysis.