Transient analysis of sliding contact of layered elastic/plastic solids with rough surfaces

 Based on the boundary element method (BEM) and a variational principle, a numerical model is developed to analyze the time – transient sliding contact of two layered elastic/plastic solids. Two cases are considered: one is the loading/sliding/unloading of a rough surface on a smooth surface, and the other is of two rough surfaces. Contact statistics, contact pressure profile and stress distribution are predicted at each time step with updated surface roughness. The results are used to study the effect of surface roughness, physical properties of the layer and the substrate, and lubricant film thickness on friction, stiction, and wear. Discussion on the integration of this contact model into advanced tribological models, e.g., wear model, is also presented. Received: 28 June 2002/Accepted: 23 October 2002 Currently at: Seagate Technology, Pittsburgh, PA Paper presented at the 13th Annual Symposium on Information Storage and Processing Systems, Santa Clara, CA, USA, 17–18 June, 2002     

Robust topology optimization of skeletal structures with imperfect structural members

A topology optimization framework is proposed for robust design of skeletal structures with stochastically imperfect structural members. Imperfections are modeled as uncertain members’ out-of-straightness using curved frame elements in the form of predefined functions with random magnitudes throughout the structure. The stochastic perturbation method is used for propagating the imperfection uncertainty up to the structural response level, and the expected value of performance measure or constraint is used to form the stochastic topology optimization problem. Sensitivities are derived explicitly using the adjoint method and are used in conjunction with an efficient gradient-based optimizer in search for robust optimal topologies. Topological designs for three representative examples are investigated with the proposed algorithm and the resulting topologies are compared with the deterministic designs. It is observed that the new designs primarily feature load path diversification, which is pronounced with increasing level of uncertainty, and occasionally member thickening to mitigate the impact of the uncertainty in members’ out-of-straightness on structural performance.     

Sensitivity analysis of frictional contact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the static frictional contact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of nodal displacements, and Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact of a composite spherical cap pressed against a rigid plate.     

A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces

The objective of this work is to develop an efficient strategy for the resolution of many configurations of a quasi-static problem with multiple contacts. Our approach is based on the multiscale LATIN method with domain decomposition. Here we propose to take advantage of the capability of the LATIN method to reuse the solution of a given problem in order to solve many similar problems. We firstly introduce the LATIN method and compare our approach to different strategies commonly used to solve contact problems. Then, we illustrate the capabilities of our method through two examples.     

Analysis of stress wave in layered structures

Numerical procedures of the method of characteristics is presented to treat the problems of multilayered structures under impulsive load. A set of eight algebraic equations which are readily to be programmed into computer are derived. Stress analysis of a typical dynamic layered structure is given to illustrate the effectiveness of the method. Results of the example problem reveal the fact that pulse shape is very sensitive to transient stress wave propagation.     

Nonlinear topology optimization of layered shell structures

Topology stiffness (compliance) design of linear and geometrically nonlinear shell structures is solved using the SIMP approach together with a filtering scheme. A general anisotropic multi-layer shell model is employed to allow the formation of through-the-thickness holes or stiffening zones. The finite element analysis is performed using nine-node Mindlin-type shell elements based on the degenerated shell approach, which are capable of modeling both single and multi-layered structures exhibiting anisotropic or isotropic behavior. The optimization problem is solved using analytical compliance and constraint sensitivities together with the Method of Moving Asymptotes (MMA). Geometrically nonlinear problems are solved using iterative Newton–Raphson methods and an adjoint variable approach is used for the sensitivity analysis. Several benchmark tests are presented in order to illustrate the difference in optimal topologies between linear and geometrically nonlinear shell structures.     

Optimal layer setup generation in layered manufacturing with a given error constraint

This paper introduces a new tolerance-based method to generate the optimum layer setup required to build layered manufacturing (LM) end-user parts for maximized efficiency. To achieve this, the deviation between the final polished LM part geometry and the original design model is formulated and controlled. Minimum build time is then realized through optimization of the thickness and position of each layer with respect to the design and final polished part geometry in order to minimize the number of layers to be used. Current LM layer setup methods target the intermediate or raw layered model, generated directly by an LM machine. By not considering the complete LM build process as well as the final polished part geometry, the involved layer setup problem cannot be correctly formulated and solved. Overly conservative layer thickness is then chosen, causing more layers than necessary to be used and greatly compromised efficiency. To achieve maximized efficiency, this work proposed a method based on error compensation and minimization. It has been applied to solving for the optimum layer setup necessary to allow the final polished physical part to meet the user-specified tolerance limit for the design model. Case studies have been performed and the results have validated that the presented method is able to minimize the number of layers for constructing an LM part while controlling the maximum error for tolerance conformance.     

Optimal design of layered structures under dynamic loading

A direct search procedure is presented to treat problems of optimization of layered structures subjected to dynamic loading conditions. The procedure combines the basic idea of the complex method of Box to locate the next trial point, with a local direct pattern search of Hooke and Jeeves to insure the continuous accelerative movement toward the optimum. The method is applied to two problems of optimal design for minimum tensile stress at the interfaces in layered structures under time-harmonic loads and transient loads, respectively.     

Optimal lot-sizing problem with imperfect maintenance and imperfect production

In this paper, we develop an integrated model for the joint determination of both economic production quantity and level of preventive maintenance (PM) for an imperfect production process. This process has a general deterioration distribution with increasing hazard rate. The effect of PM activities on the deterioration pattern of the process is modelled using the imperfect maintenance concept. In this concept, it is assumed that after performing PM, the ageing of the system is reduced in proportion to the PM level. After a period of time in production, the process may shift to out-of-control states, either type I or type II. A minimal repair will remove the type I out-of-control state. If a type II out-of-control state occurs, the production process has to stop, and then restoration work is carried out. Examples of Weibull shock models are given to show that the use of PM reduces costs.     

A Linguistic Possibility-Probability Aggregation Model for decision analysis with imperfect knowledge

Knowledge which is imperfect creates obstructions in the operational parameter setting (OPS) of the functions of decision making; however it is relatively inexpensive to obtain the data to fill the knowledge gap by taking subjective measures. The collection of human experience data through individual subjective assessments tends to be aggregated as being of more objective value. This paper proposes a Linguistic Possibility-Probability Aggregation Model (LPPAM) to address this problem of OPS. LPPAM includes a Compound Linguistic Ordinal Scales model as a rating interface to improve the quality of data collection. The CLOS model addresses the problems with consistency, such as in the linguistic choices, accuracy of linguistic representation of numbers and bias of rating dilemmas. LPPAM also contains a multi-expert and multi-attribute aggregation model, which is to derive meaningful arguments fitting the setting of operation parameters. Five algorithms are used for LPPAM. The significance of LPPAM is that it can be applied in group multi-criteria decision problems and large scale survey systems. To validate the proposed framework, with a comparison with the Analytical Network Process (ANP), a R&D project selection problem is given.     

Topology optimization of structures in unilateral contact

In this paper a general framework for topology optimization of structures in unilateral contact is developed. A linear elastic structure that is unilaterally constrained by rigid supports is considered. The supports are modeled by Signorini’s contact conditions which in turn are treated by the augmented Lagrangian approach as well as by a smooth approximation. The latter approximation must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equation and the two different contact formulations, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problems are solved by SLP. This is done by using a nested approach where the state equations are linearized and sensitivities are calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D as well as in 3D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.     

Long-time behavior of PML absorbing boundaries for layered periodic structures

In this work we consider a special case of the Perfectly Matched Layer (PML) divergence which is observed by the simulation of the planar periodic structures such as photonic crystal slabs or antenna arrays. This divergence is caused by an excitation of long-living artefact evanescent waves in these structures by an incident external pulse. We study the application of the known remedies to this problem: increasing the distance between the structure and PML, employing the κ parameter, employing non-PML absorbers. We also suggest a new simple and effective solution, where the usual PML is backed by an additional absorbing layer.     

Collapse load evaluation of structures with frictional contact supports under combined stresses

This paper extends classical limit analysis to structures for which some supports are subjected to “nonstandard” unilateral frictional contact with the ground. A typical and commonly adopted model is nonassociative Coulomb friction. For such cases, the use of the classical bound theorems is not possible. Moreover, simply solving the governing equations as a mixed complementarity problem (MCP) does not guarantee that the best bound has been calculated. We have therefore developed an approach that attempts to compute, in a single step, the critical (least) upper bound solution by formulating and solving an instance of the challenging class of optimization problems, known as a mathematical program with equilibrium constraints (MPEC). Two examples are provided to illustrate application of the proposed scheme, as well as to highlight some key features of such structures.     

Software development with imperfect information

Delivering software systems that fulfill all requirements of the stakeholders is very difficult, if not at all impossible. We consider the problem of coping with imperfect information, like interpreting incomplete requirement specifications or vagueness in decisions, one of the main reasons that makes software design difficult. We define a method for tracing design decisions under imperfect information. To model and compare requirements with estimations, we present fuzzy and stochastic techniques. This approach offers adequate decision support that can deal with imperfect information during software design. The approach is illustrated by a real-world example, based on a storm surge barrier system.     

Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge

A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.     

A multiresolution homogenization of modal analysis with application to layered media

We apply multiresolution techniques to study the effective properties of boundary value problems. Conditions under which boundary values are preserved in the effective (‘homogenized') formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic formulation and those of the effective formulation are explored. Applications to the construction of effective Green function in a complex lamination are discussed. The analytic results are demonstrated via numerical computations.     

Analysis and optimal design of layered structures subjected to impulsive loading

The attenuation of elastic stress waves propagating through layered structures situated between free and fixed surfaces is investigated. A stress transfer function, which relates the stress response at the fixed support to the applied stress pulse, is derived for several specific layered structures. An analysis of these responses indicate that when an incident stress pulse passes through a layered structure, a reduced stress amplitude and elongated pulse duration could be obtained with proper selection of materials and layer dimensions. Consequently, a design procedure is proposed to obtain the optimal layered structure, and several specific cases of layered structures are investigated.     

面向三维层面网格生成的层序分析方法研究

在地震数据处理中,通过在地震数据体中人工拾取同相轴建立地层三维模型,这一过程费时费力。为解决该问题,提出了一种利用同相轴自动追踪结果的层序分析算法,该方法将自动追踪结果的分类问题,转化为给自动追踪结果排序的问题,并利用最小二乘法求全局最优排序。使用排序的结果可以恢复追踪结果的拓扑信息,从而直接用于层面网格建模。实验结果表明了该方法用于生成层面网格的有效性,其计算结果符合实际的地质状况。     

Numerical analysis and simulations of contact problem with wear

This paper presents a quasistatic problem of an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. We recall existence and uniqueness results obtained in Sofonea et al. (2017). The main aim of this paper is to present a fully discrete scheme for numerical approximation together with an error estimation of a solution to this problem. Finally, computational simulations are performed to illustrate the mathematical model.