Shape optimization for elasto-plastic deformation under shakedown conditions

An integrated approach for all necessary variations within direct analysis, variational design sensitivity analysis and shakedown analysis based on Melan’s static shakedown theorem for linear unlimited kinematic hardening material behavior is formulated. Using an adequate formulation of the optimization problem of shakedown analysis the necessary variations of residuals, objectives and constraints can be derived easily. Subsequent discretizations w.r.t. displacements and geometry using e.g. isoparametric finite elements yield the well known ‘tangent stiffness matrix’ and ‘tangent sensitivity matrix’, as well as the corresponding matrices for the variation of the Lagrangian-functional which are discussed in detail. Remarks on the computer implementation and numerical examples show the efficiency of the proposed formulation. Important effects of shakedown conditions in shape optimization with elasto-plastic deformations are highlighted in a comparison with elastic and elasto-plastic material behavior and the necessity of applying shakedown conditions when optimizing structures with elasto-plastic deformations is concluded.     

Identification of adhesive properties in GLARE assemblies using digital image correlation

An experimental-numerical methodology is introduced to identify the parameters of a cohesive law of an adhesive layer within a joined assembly on the basis of kinematic data provided by digital image correlation. Non-conventional experiments on joined samples were designed to generate within the assembly and the adhesive film complex strain and stress states close to those expected in-service and up to complete debonding. The modeling is developed with reference to the observed sub-domain in which the experimental boundary conditions are prescribed. The nonlinear behavior of the adhesive layer is described as a finite-thickness interface endowed with a mixed-mode cohesive law whose parameters are identified so as to match at best the measured displacement field.     

A New Study on the Relative Kinematic Accuracy Reliability of a Novel Exoskeleton with Series-Parallel Topology

An excellent exoskeleton worn by the operator might be able to move with a high degree of accuracy and repeatability. Based on the previous kinematic accuracy reliability model, this article proposes two new definitions of the relative kinematic accuracy reliability to investigate the motion accuracy ability of a novel exoskeleton with series-parallel topology thoroughly. According to the new definitions, the calculating results show that x-, y-, and z-directions of the exoskeleton end-effector have different motion accuracy abilities, the motion accuracy ability of x is the best of all, and the motion accuracy ability of y is better than that of z. To study error sources, we illustrated the geometric tolerances and driving errors, which cause the uncertainties of the exoskeleton end-effector. The effects of geometric tolerances and driving errors on kinematic accuracy reliability and relative kinematic accuracy reliability, which are the sensitivity analyses, were numerically simulated and elucidated. The results reveal that the error sensitivity in the x-direction is the lowest and the error sensitivity in the y-direction is lower than that in the z-direction. Besides this, the effects of driving errors on the motion ability of all directions of the exoskeleton end-effector are larger than those of geometric tolerances. This approach for modeling and calculating kinematic accuracy reliability, relative kinematic accuracy reliability, and their sensitivity analysis provides a novel and unique reference standard for exoskeleton and other mechanism design.     

A multi-body optimization framework with a knee kinematic model including articular contacts and ligaments

Multi-body optimization is one of the methods proposed to reduce the errors due to soft-tissue artifact in gait analysis based on skin markers. This method uses a multi-body kinematic model driven by the marker trajectories. The kinematic models developed so far for the knee joint include a lower pair (such as a hinge or a spherical joint) or more anatomical and physiological representations including articular contacts and the main ligaments. This latter method allows a better representation of the joint constraints of a subject, potentially improving the kinematic and the subsequent static and dynamic analyses, but model definition and mathematical implementation can be more complicated. This study presents a mathematical framework to implement a kinematic model of the knee featuring articular contacts and ligaments in the multi-body optimization. Two penalty-based methods (minimized and prescribed ligament length variations) consider deformable ligaments and are compared to a further method (zero ligament length variation) featuring isometric ligaments. The multi-body optimization is performed on one gait cycle for five asymptomatic male subjects by means of a lower limb model including the foot, shank, thigh and pelvis. The mean knee kinematics, ligament lengthening and contact point positions are compared over the three methods. The results are also consistent with results from the literature obtained by bone pins or biplanar fluoroscopy. Finally, a sensitivity analysis is performed to evaluate how the joint kinematics is affected by the weights used in the penalty-based methods. The approach is purely kinematic, since the penalty-based framework does not require the solution of the joint static or dynamic analyses and makes it possible to consider ligament deformations without the definition of ligament stiffness that generally cannot be identified through in vivo measurements. Nevertheless, as far as a knee kinematic model is concerned, particularly in musculoskeletal modeling, this approach appears to be a good compromise between standard non-physiological kinematic models and complex deformable dynamic models.     

Analysis of prestressed mechanisms

A new theory is presented for the matrix analysis of prestressed structural mechanisms made from pin-jointed bars. The response of a prestressed mechanism to any external action is decomposed into two almost separate parts, which correspond to extensional and inextensional modes. A matrix algorithm which treats these two modes separately is developed and tested. It is shown that the equilibrium requirements for the assembly, in its initial configuration as well as in deformed configurations which are obtained through infinitesimal inextensional displacements, can be fully described by a square equilibrium matrix. It is also shown that any set of extensional nodal displacements has to satisfy some equilibrium conditions as well as standard compatibility equations, and that the resulting system of linear equations defines a square kinematic matrix. Theoretical as well as experimental evidence supporting this approach is given in the paper ; two simple experiments which were of crucial importance in arriving at the equilibrium conditions on the extensional displacements are described.The interaction between the two modes of action of a prestressed mechanism is discussed, together with a rapidly converging iterative procedure to handle it. A study of the non-linear effect by which the self-stress level in a statically indeterminate assembly rapidly increases if an inextensional mode is excited, supported by further experimental results, concludes the paper. This work is relevant to the analysis of most cable systems, pneumatic domes, fabric roofs, and “Tensegrity” frameworks.     

Design Sensitivity Analysis of Truss Structures with Elastoplastic Material*

ABSTRACT

A continuum-based design sensitivity analysis (DSA) method is presented for configuration (or layout) design of nonlinear structural systems with rate-independent elastoplastic material. Configuration design variables are characterized by shape and orientation changes of the structural component. A continuum-based shape DSA method that utilizes the material derivative of continuum mechanics is extended to account for effects of shape and orientation variations. The incremental analysis method, with updated Lagrangian formulation, is used to derive the design sensitivity for the nonlinear structural system.

To derive the design sensitivity, incremental energy and load forms are utilized. The first variations of energy and load forms and the static response with respect to configuration design variables are described using the material derivative. Direct differentiation is utilized to obtain the first variation of the performance measure explicitly in terms of variations of configuration design variables. With the consistent tangent stiffness matrix employed at the end of each load step to compute the design sensitivity, it is found that no iterations are necessary to compute design sensitivity. In addition, the linear design velocity is used to account for configuration design changes, with the velocity field being updated at each load step of the incremental analysis.     

The structural performance of the periodic truss

Matrix methods of linear algebra are used to analyse the structural mechanics of the periodic pin-jointed truss by application of Bloch's theorem. Periodic collapse mechanisms and periodic states of self-stress are deduced from the four fundamental subspaces of the kinematic and equilibrium matrix for the periodic structure. The methodology developed is then applied to the Kagome lattice and the triangular-triangular (T-T) lattice. Both periodic collapse mechanisms and collapse mechanisms associated with uniform macroscopic straining are determined. It is found that the T-T lattice possesses only macroscopic strain-producing mechanisms, while the Kagome lattice possesses only periodic mechanisms which do not generate macroscopic strain. Consequently, the Kagome lattice can support all macroscopic stress states. The macroscopic stiffness of the Kagome and T-T trusses is obtained from energy considerations. The paper concludes with a classification of collapse mechanisms for periodic lattices.     

多孔材料塑性极限载荷及其破坏模式分析

运用塑性力学中的机动极限分析理论，研究韧性基体多孔材料的塑性极限承载能力和破坏模式。以多孔材料的细观结构为研究对象，将细观力学中的均匀化理论引入到塑性极限分析中，并结合有限元技术，建立细观结构极限载荷的一般计算格式，并提出相应的求解算法。数值算例表明：细观孔洞对材料的宏观强度影响明显；在单向拉伸作用下，孔洞呈现膨胀扩大规律；多孔材料破坏源于基体塑性区的贯通。     

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前手翻屈体前空翻2周是男子跳马最高难度动作之一. 迄今,我国只有胡俊捷曾完成 该动作. 本文通过三维运动学分析技术揭示了胡俊捷完成前手翻屈体前空翻2周动作的运动 学规律与技术特点,获得了身体重心和主要关节的位移,水平速度和垂直速度及关节角度等 运动学指标的变化. 这些结果可为我国运动员发展和改进此类动作提供理论依据和技术参 考.     

Analysis of linear elastic wave propagation in piping systems by a combination of the boundary integral equations method and the finite element method

The combined methodology of boundary integral equations and finite elements is formulated and applied to study the wave propagation phenomena in compound piping systems consisting of straight and curved pipe segments with compact elastic supports. This methodology replicates the concept of hierarchical boundary integral equations method proposed by L. I. Slepyan to model the time-harmonic wave propagation in wave guides, which have components of different dimensions. However, the formulation presented in this article is tuned to match the finite element format, and therefore, it employs the dynamical stiffness matrix to describe wave guide properties of all components of the assembled structure. This matrix may readily be derived from the boundary integral equations, and such a derivation is superior over the conventional derivation from the transfer matrix. The proposed methodology is verified in several examples and applied for analysis of periodicity effects in compound piping systems of several alternative layouts.     

Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. Sensitivity analysis and mode-I parameter identification

The identification of mode-I parameters of a cohesive-zone model for the analysis of adhesive joints is presented. It is based on an experimental–numerical methodology whereby the optimal parameters are obtained as the solution of a nonlinear programming problem. The data set for inverse analysis is provided either by local kinematic data, by global static data, or a combination of the two. Parameter sensitivities are computed via direct differentiation and identification exercises are discussed that show the effectiveness of the procedure and its stability with respect to noise and time–space sampling.     

Benchmarking of adjoint sensitivity-based optimization techniques using a vehicle ride case study

Several studies on multibody dynamics optimization have been conducted. One important limitation of these studies is their computational e?ciency, especially when optimizing a complex system’s performance. The co-authors developed a very e?cient optimization technique based on an adjoint sensitivity analysis methodology. The scope of this article is to validate this technique by conducting a benchmark analysis against some of the most popular optimization methods, including gradient-based optimization using finite differences, design of experiment using optimal Latin hypercube, and design of experiment using full factorial design matrix. A vehicle system is used as a case study for optimizing its ride comfort.     

Kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator used for controllable pitch propeller

This article investigates the kinematic modeling and dexterity evaluation of a PS-RRS-2RUS parallel manipulator. The design concept and mobility analysis of the manipulator are first addressed utilizing the screw theory. Second, the decoupled and closed-form kinematic solutions with multiple configurations are solved through vector method. Then, the analytical expressions for the velocity relationships are derived into a closed-form Jacobian matrix, which is then used to distinguish the singular postures. Finally, the workspace with fixed orientation is calculated and its dexterity is evaluated. The numerical simulations and validation are conducted in a case study.     

POD-identification reduced order model of linear transport equations for control purposes

Intrusive reduced order modeling techniques require access to the solver's discretization and solution algorithm, which are not available for most computational fluid dynamics codes. Therefore, a nonintrusive reduction method that identifies the system matrix of linear fluid dynamical problems with a least-squares technique is presented. The methodology is applied to the linear scalar transport convection-diffusion equation for a 2D square cavity problem with a heated lid. The (time-dependent) boundary conditions are enforced in the obtained reduced order model (ROM) with a penalty method. The results are compared and the accuracy of the ROMs is assessed against the full order solutions and it is shown that the ROM can be used for sensitivity analysis by controlling the nonhomogeneous Dirichlet boundary conditions.     

Kinematic variables bridging discrete and continuum granular mechanics

It is known that there is wide, and at present, unbridgeable, gap between discrete and continuum granular mechanics. In this contribution, first, microscopic kinematic variables neglected in classical continuum granular mechanics are investigated based on the kinematics of discs in contact. Then, a kinematic variable called the averaged pure rotation rate (APR) is proposed for an assembly of circular discs of different sizes, which is then used to produce another two kinematic tensors with one equal to the deformation rate tensor and the other unifying the spin tensor and the APR. As an example, the kinematic variables are incorporated into the unified double-slip plasticity model. Finally, these theoretical analyses are verified using a two-dimensional discrete element method. The study shows that these kinematic variables can be used to bridge discrete and continuum granular mechanics.     

Design of a 6-DOF force device for virtual assembly (FDVA-6) of mechanical parts

Among different interaction modalities, force feedback is one of the key technologies to increase the interactivity and immersion of a virtual assembly process. This paper presents a 6-DOF force device with its forward kinematic analysis, workspace simulation, and gravity compensation. To evaluate the device, a prototype system is developed and a case study is conducted to assemble a mechanical product. The users have given positive feedback on the gravity compensation implemented and the general performance of the device.     

On Uniqueness in the Elastoplastic Analysis of Frames

ABSTRACT

A very simple example of elastoplastic analysis is adduced to illustrate how more than one deformed configuration can be associated with a single prescribed load state. The encoding of holonomic elastoplastic analysis in quadratic programming form leads to an uniqueness theorem for the bending moments (static solution), and yet, even for holonomic elastoplasticity, the uniqueness of the deformed configuration (kinematic solution) cannot be guaranteed. Different kinematic solutions, when they exist, are seen from the simple example to be physically induced by different load paths terminating at the same prescribed load state, and thus it is proved that holonomic elastoplasticity is not strictly path independent. Any two valid kinematic solutions can only differ by the motion of a special mechanism, called a pseudo-mechanism. This device is used to establish a uniqueness theorem for the kinematic solution obtained by quadratic programming or any other form of holonomic elastoplastic analysis. Finally, it is shown that load states exhibiting non-unique kinematic solutions always He on pseudomechanism lines in load space, and that a load path which lies along some part of such a line produces a completely indeterminate deformed configuration.     

机器人通过奇点的运动学逆问题的数值解法

机器人在完成其规划动作时,常可能要通过其运动链的奇点,这时求解其运动学逆问题的通用算法遇到本质的困难,本文给出了一种算法,它可以成功地克服这个困难。文中还给出了计算实例。     

A methodology to achieve the set of operation modes of reconfigurable parallel manipulators

The demand for increasingly more versatile machinery has boosted the development of the so-called reconfigurable mechanisms. In this paper, the authors present a general methodology to assess the multioperational capacity of a 6-DOF parallel manipulator basing on the possible motion patterns having Lie group structure that the manipulator owns. This ability of having different operation modes enables the manipulator to adapt to diverse tasks. To show the potential of the methodology, this approach has been applied to the 6-DOF 3-CPCR which is capable of generating multiple motion patterns. In addition to carrying out the complete theoretical study in which all the different operation modes are obtained, and validating the procedure with GIM software designed for kinematic analysis and design of mechanisms, a demonstration prototype of the 3-CPCR parallel manipulator has been also built.