Showing papers in "Mechanics Based Design of Structures and Machines in 2003"

Design of Distributed Compliant Mechanisms

Abstract: The optimization problem formulations currently used to synthesize compliant mechanism topologies aim to maximize the flexibility for obtaining the desired output motion while maximizing the overall stiffness for satisfactorily bearing the applied loads. The best solution to this problem, as posed, is a linkage consisting of rigid members connected together with revolute joints. The current elastic mechanics-based formulations do generate compliant topologies that closely imitate a rigid-body linkage by means of lumped compliance as in flexural pivots. Systematically generating such topology solutions could serve as a creative aid in the conceptual design of mechanisms, especially when the force-deflection specifications are nonintuitive to human designers. However, flexural pivot-based compliant designs are not useful in most applications when large displacements and/or high strength are desired. Ideally, compliant designs should distribute flexibility uniformly throughout the structure rather t...

Multibody Simulation Model of Human Walking

Abstract: A three-dimensional simulational model of a human walking is presented. The biped is anthropomorphic, i.e., its inertial and kinematical properties are similar to human ones. The biped consists of eight rigid bodies. Each leg consists of three parts: thigh, shank, and foot. The trunk is modeled as two rigid bodies connected by a revolute joint. The inertia properties of head and arms are included in trunk properties. Each leg has 7 degrees of freedom. The whole modelled biped has 21 degrees of freedom. The impact and friction effects are considered in the ground reaction force modeling. The ground is represented by a flat, rigid surface. The normal to the ground component of reaction force depends on penetration of the foot into the ground and on the velocity of this penetration. The tangential reaction is represented in terms of a pseudo-Coulomb friction model (in this model of friction there is no stiction phase, i.e., the bodies are moving relative to each other at a negligibly small velocity)...

Solution of Redundant Muscle Forces in Human Locomotion with Multibody Dynamics and Optimization Tools

Abstract: The analysis of human motion using inverse dynamics approaches allows for the evaluation of the muscle forces based on the knowledge of the kinematics of the human subject and the applied external forces. Owing to the redundant nature of the muscle arrangement, the system of equations available for the solution of the inverse dynamics problem has more unknown muscle forces than available equations. Therefore static optimization techniques are required to obtain a solution of the problem. Emphasizing applications to gait analysis and normal sports activities a whole-body, three-dimensional, biomechanical model of the human muscle-skeletal system is purposed to support the inverse dynamic analysis. In its current state of development, the biomechanical model includes a detailed description of the principal muscles of the locomotion apparatus for the lower limbs while net moments-of-force are used to represent the lumped muscle action about each other anatomical joint of the model. The muscles used ...

Uncertainty Propagation Using Possibility Theory and Function Approximations

Abstract: Based on the nature and extent of uncertainty existing in an engineering system, different approaches can be used for uncertainty propagation. If the uncertainty of the system is due to imprecise information, and lack of statistical data, the Possibilistic theory can be used. During preliminary design, uncertainties need to be accounted for and due to lack of sufficient information, assigning a probability distribution may not be possible. Moreover, the flight conditions (loads, control surface settings, etc.) during a mission could take values within certain bounds, which do not follow any pattern. The uncertain information in these cases is available as intervals with lower and upper limits. In this case, the fuzzy-arithmetic-based method is suitable to estimate the possibility of failure. The use of surrogate models to improve the efficiency of prediction is presented in this article. Various numerical examples are presented to demonstrate the applicability of the method to practical problems.

State-Space Generalized Predictive Control for Redundant Parallel Robots

Abstract: The article deals with the design and properties of generalized predictive control (GPC) for path control of redundant parallel robots. Redundant parallel classification means redundant number of actuators, i.e., more actuators than degrees of freedom of the robot. Control of such structures suffers from several new control problems like potential inconsistency of steady state positions or nonuniqueness of control actions. The article explains classical direct derivation of GPC and its modification based on square root two-step design of control actions for solving the control problems. As an example for verification of algorithms, a prototype of a planar redundant parallel robot is used. Both design approaches are compared and several possibilities of extensions are presented for taking into consideration additional requirements, like smooth course of actuators or fulfillment of the anti-backlash condition.

On the elastic-plastic deformation of a rotating disk subjected to a radial temperature gradient

Abstract: Elastic–plastic stress distribution in a nonisothermal rotating annular disk is analyzed by the use of Tresca and von Mises criteria. An energy equation that accounts for the convective heat transfer with a variable heat transfer coefficient is modeled. For a given angular velocity, the steady temperature distribution in the disk is obtained by the analytical solution of the energy equation. Tresca yield criterion and its associated flow rule are used to obtain the analytical stress distributions for a linearly hardening material. A computational model is developed to analyze elastic–plastic deformations of the disk using von Mises yield criterion and its flow rule. This model incorporates Swift's hardening law to simulate linear as well as nonlinear hardening material behavior. It is shown that the stress distribution in the disk is affected significantly by the presence of the temperature gradient.

Simulation of Railway Vehicles: Necessities and Applications

Abstract: During recent years, the computational simulation of a railway vehicle's running behavior has grown to a kind of standard design task in the railway industry. Well-qualified for this kind of computational process are software tools for the simulation of general mechanical and mechatronic systems based on a multibody system approach. But for their effective application to arbitrary wheel–rail systems a couple of specific modeling features have to be available, of which an efficient modeling of a steel wheel in contact with a steel rail is the most important one. The article gives a brief insight into the modeling of railway vehicles with the focus concentrating on a generally applicable wheel–rail contact module. The basic principles of this module are a so-called quasi-elastic contact model together with a description of the wheel–rail interface as a kinematic constraint. As specific application case, the demanding simulation of a railway vehicle running through a switch is presented.

Solving Nonconvex Problems of Multibody Dynamics with Joints, Contact, and Small Friction by Successive Convex Relaxation

Abstract: Time-stepping methods using impulse-velocity approaches are guaranteed to have a solution for any friction coefficient, but they may have nonconvex solution sets. We present an example of a configuration with a nonconvex solution set for any nonzero value of the friction coefficient. We construct an iterative algorithm that solves convex subproblems and that is guaranteed, for sufficiently small friction coefficients, to retrieve, at a linear convergence rate, the velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled. In addition, we show that one step of the iterative algorithm provides an excellent approximation to the velocity solution of the original, possibly nonconvex, problem if the product between the friction coefficient and the slip velocity is small.

Railway Vehicle Dynamics: Some Aspects of Wheel–Rail Contact Modeling and Optimization of Running Gears

Abstract: A significant part of a computer-aided model of a railway vehicle is the description of forces at contact between wheel and rail. Computation of these forces is one of the most time-consuming CPU operations during the simulation process. Mathematical models of the contact forces often lead to stiff equations of motion because of high contact stiffness. In this article, an approximate, nonstiff method for computing the nonelliptical contact problem and some results of its implementation are presented. Optimization of multibody systems is presented as a multicriteria optimization problem. The problem of forming objective function is still open due to wide variety of conflicting criteria, which have to be reduced to a scalar function. Implementation of an approach for optimizing dynamic systems based on the analytic hierarchy process for getting the scalar objective function is presented. The application of the developed approach to railway vehicle dynamics is considered.

Analysis of machining stability for a parallel machine tool

Abstract: Machine tool chatter is a self-excited vibration generated by chip thickness variation. It severely degrades the quality of the machined surface. The incidence of chatter is greatly affected by the dynamic characteristics of machine tool structure. This article extends chatter stability analysis to a machine tool equipped with a parallel mechanism. The vibration model of a parallel machine tool is derived, in which the legs of the parallel mechanism are considered as spring-damper systems. Then, the regenerative cutting dynamics is combined with the vibration model and stability analysis is performed. The chatter stability charts for various machining parameters are examined, with the example of the cubic parallel mechanism that is specially designed for machine tool use.

Layout Optimization of Rigid-Plastic Structures Under High Intensity, Short-Time Dynamic Pressure

Abstract: The layout optimization method of rigid-plastic structures (plates, shells, frames, trusses) is based on the assumption that the high intensity, short-time dynamic pressure can be replaced by impulsive loading represented by an initial velocity field. The concept of porous material is used where the material distribution is described by the densities of the finite elements that are the design variables. To control the plastic behavior of the structure, an upper bound theorem is used for the determination of the expected moderately large residual displacements. In the design, the effect of strain rate sensitivity is also taken into account. The aim of the design is to minimize the mass of the structure. The formulation of the method leads to two nonlinear mathematical programming problems coupled by the design variables. The solution can be obtained by iteration. The application is illustrated by numerical examples.

Probabilistic-Guaranteed Optimal Design of Membrane Shells Against Quasi-brittle Fracture

Abstract: The problems described in this article concern the shape optimization of brittle or quasi-brittle (axisymmetric) elastic shells. The optimization problem takes into consideration the possibilities of cracks arising and consists in finding the shape of the shell loaded by external forces in such a way that the cost function (volume of the shell material) reaches a minimum, while satisfying some prescribed bounds on stress intensity factors. The questions discussed are characterized by incomplete information concerning crack size, crack location, and its orientation. In this context, the article presents some formulations of optimal shell design problems based on probabilistic-guaranteed approach and provides some results of analytical investigation for thin-walled shells with a through cracks.

Efficient Modal Approach for Flexible Multibody Dynamic Simulation

Abstract: A flexible body formulation is presented for efficient flexible multibody dynamic simulation of mechanical systems that contain large-scale, finite-element, flexible body models. With this formulation, the equations of motion of flexible bodies, as well as their linearized form required for implicit integration, are expressed such that all terms that depend on the dimension of the finite-element models of flexible bodies can be evaluated in a preprocessing stage. This enables efficient simulation, even with very detailed finite-element models that are found in industrial applications.

Analogy Between Bifurcations in Stability of Structures and Kinematics of Mechanisms

Abstract: This article discusses singularities occurring in compatibility paths of planar bar-and-joint mechanisms with 1 degree-of-freedom. Bifurcation of branches of compatibility paths are examined and simple examples are given for several bifurcation modes. Effects of geometric imperfections on the kinematic behavior are also considered. The behavior and properties of kinematic bifurcations are paralleled to those of equilibrium bifurcations known in stability theory. An analogy is presented between the two areas incorporating the different types of bifurcation, effects of imperfections, and detection of singularities. A formulation of potential energy for mechanisms is also proposed in analogy with the potential energy function used in structural analysis.

Fatigue Strength Evaluation on Resistance Spot Welds of the Vehicle Body

Abstract: This article evaluates the fatigue stress–fatigue life relationship of spot-welded structures in the vehicle body, considering the residual stress effect When a vehicle travels on an actual road, the resistance spot welds of the vehicle structure are exposed to complex loadings Because fatigue strength in the resistance spot weld of a vehicle body can be determined by residual stresses, joint geometry, and loading state during driving, actual loading state must be estimated with consideration of residual stresses In this study, fatigue stress–fatigue life relationship derived from residual stress was obtained by thermoelastic, plastic, finite-element analysis Applied loading in resistance spot weld of the vehicle body was calculated by dynamic analysis Assumptions regarding fatigue life were based on proposed methods

Optimization of Submerged Funicular Arches

Abstract: This paper is concerned with the least weight design of fully stressed, funicular arches subjected to hydrostatic forces and selfweight and having supporting points on different elevations. The optimization problem is posed as the minimization of the arch weight with respect to the axial force parameter, the initial slope of the arch shape and the total curved arch length. To be satisfied is the inequality constraint that is constructed from the error norm to be within a specified tolerance value. This error norm is the sum of the absolute values of the differences between the desired terminal boundary conditions and the computed ones obtained from performing a forward integration of the governing set of first-order differential equations defining the funicular arch shape. The generalized reduced gradient nonlinear optimization method was adopted for the optimization process. Optimal funicular shapes of submerged arches are presented for various water depths, selfweight parameters, and ground slo...

Modeling and Simulation of Elastoplastic Multibody Systems with Damage

Abstract: Flexible multibody systems are studied where plasticity is induced by inertial forces. Such a situation may occur when the stiffness of a structure is weakened by an operation under catastrophic environmental conditions. To analyze this phenomenon, plane motions of beam elements with large rigid-body motion and moderately large deformation are considered. The equations of motions for the problem are derived by Hamilton's principle extended to nonconservative systems. Stiffening terms are included via the second order theory of structures. The elastic part of the multibody system generates differential algebraic equations (DAE). Implicit Runge Kutta schemes are used to transform the DAEs into a nonlinear system of equations that have to be solved for every time-step. The nonlinear part of strain is solved by a fixed-point iteration, where the nonlinear system of equations is solved in every step of the iteration. The high efficiency of this method is due to the fact that the fixed-point iteration ...

Contact Simulation for Many Particles Considering Adhesion

Abstract: This article deals with the calculation and administration of contact between many moving bodies in the planar case. The main issue is the contact determination between bodies of either round or polygonal shape. The modeling is done by means of molecular dynamics to investigate the motion of many bodies very efficiently. Besides elastic normal forces, which prevent penetration of the bodies, damping forces and adhesion is described and considered for the computations. Our interest is directed toward collision detection. By means of sorting algorithms, neighboring bodies are found easily and, therefore, systems consisting of a large number of bodies can be determined efficiently.

Some probabilistic problems of beam and frame optimization under longevity constraint

Abstract: The questions investigated in this article are related to an important class of problems of optimal structural design concerning the shape optimization of quasibrittle elastic bodies with cracks. The optimization problems taken into consideration consist of finding the boundary of a body loaded by cyclic quasistatical forces in such a way that the cost functional (volume of the body) reaches a minimum, while satisfying some prescribed bounds on structural longevity (i.e., on the number of cycles before destruction). These problems are characterized by incomplete information concerning initial crack size and location. In this context, the article presents some possible formulations of optimal structural problems, based on probabilistic approaches, and some examples of analytical solutions.

Stabilization of Constraints of Multibody System Dynamics

Abstract: Numerical algorithms for the solution of nonlinear algebraic equation systems are discussed. Special application to the mechanism and multibody system kinematic analysis, as well as to the problems of constraint stabilization during dynamics simulation is regarded. Special attention is paid to the approaches of a separate solution of the differential equations and constraint stabilization. Numerical procedures that are effective additions to the well-known algorithms based on the Newton-Raphson method are presented. The problems of loss of precision and achievement of large unreal increments of the varying parameters are discussed. The traditional Newton-Raphson method is modified by applying a step reduction procedure that is developed numerically for the symbolic form of kinematic and dynamic equations. An optimization method for stabilization of constraints using the mass matrix of dynamic equations is suggested. According to the objective function defined the stabilization procedure provides ...

Buckling of a Circular Plate with Internal Elastic Ring Support

Abstract: The buckling from radial edge pressure of a thin circular plate with internal concentric elastic ring support is studied. The buckling load obtained from the exact characteristic equation shows complicated mode switches between axisymmetric and asymmetric buckling modes. The optimum radius of the internal support is also found.

Active Noise Control Using Piezoelectric Actuators in Hard Disk Drives

Abstract: With the increasing use of electromechanical microsystems, such as hard disk drives, CD-ROM drives, and DVD drives in the consumer electronics industry, there is a growing demand for quieter products. The noise emitted from these devices may originate from the vibration of mechanical components in operation, such as bearings, gears, and actuators. The vibration is then transmitted to other parts of the device, such as the covers, and the noise emitted may then be amplified. The objective of this article is to find a way to control seek noise in hard disk drives. Piezoelectric actuators are attached to the cover, which are used to excite the cover and suppress noise transmission of the cover of hard disk drives. A controller feedback of vibration observes through piezoelectric sensors and adjusts the voltage inputs to the actuators to minimize the radiated sound level. To get the optimal piezoelectric actuator location, genetic algorithms with immune diversity are adopted. Numerical results show t...

On Displacement Analysis of the RSSR-SS Mechanism

Abstract: This article presents a method for performing (RSSR-SS) mechanism displacement analysis. The benefit of this method is that it provides a practical alternative for performing RSSR-SS mechanism displacement analysis and is fully applicable with today's mathematics software. This method is an extension of the adjustable RSSR-SS synthesis method developed by the authors (Suh, C. H., Radcliffe, C. W. (1978). Kinematic analysis of spatial mechanisms. In: Kinematics and Mechanism Design. New York: John Wiley and Sons, pp. 179–183). By utilizing the passive degree of freedom of the coupler of the RSSR mechanism and its design equations (Sandor, G. N., Erdman, A. G. (1984). Spatial mechanisms with an introduction to robotics. In: Advanced Mechanism Design Analysis and Synthesis. Englewood Cliffs: Prentice-Hall, pp. 635–641), the design equation for the remaining (S-S) link of the RSSR-SS mechanism was developed using spatial transformation matrices under the constant length condition of the remaining S-S...

Hybrid Recursive Formulation for Efficient Dynamic Simulation of General Multibody Systems

Abstract: In this study, the development of a hybrid recursive formulation alternatively executing the modified recursive algorithm or the fully recursive algorithm automatically for computational efficiency is introduced for general multibody systems. To enable the hybrid recursive formulation, we divided the global system into subsystems. To switch algorithms easily between the subsystems, we adjusted the modified recursive algorithm and the fully recursive algorithm to have the same definition of velocity state vector. These modifications increase the numerical efficiency of each algorithm. Analysis in the hybrid recursive formulation consists of subdivisions of the systems and selection between the fully recursive algorithm and the modified recursive algorithm, depending on the type of each subsystem. A broad range of numerical tests show this hybrid formulation is very efficient: It is as efficient as the modified recursive formulation in highly constrained parallel systems and has a linear property w...

A Multi-objective Heuristic-Based Hybrid Genetic Algorithm

Abstract: Most attempts by researchers to improve upon multi-objective genetic algorithms (MOGAs) involve different implementations of the traditional genetic algorithm operations (i.e., fitness assignment, crossover, and mutation). However, adherence to models that remain consistent with evolutionary theory may be stifling further performance gains that could be realized through the development of hybrid algorithms. This paper presents a hybrid MOGA that combines a baseline MOGA with heuristics specifically tailored to address deficiencies often encountered in multi-objective optimization. The new hybrid technique is compared to the baseline MOGA in its application to a two-objective two-bar truss design and a three-objective packaging design of a power electronic module. The comparison is aided by four recently developed metrics that provide a balanced quantitative measurement of performance. The new technique was shown to consistently outperform the baseline MOGA for the application examples. *Communica...

Vibration of a Rigid Body Suspended by Taut Strings

Abstract: A solid body is suspended by equally spaced taut strings. The characteristic equations for small vibrations of the system are formulated exactly. Depending on the mass and moment of inertia parameters of the body, the fundamental frequency may be governed by either the symmetric mode or the antisymmetric mode.

A Theoretical Analysis on the Deformation of Rectangular Plate Under Out-of-Plane Tearing

Abstract: A theoretical analysis is proposed to predict the out-of-plane tearing response of rectangular plates with two or three legs. The nonlinear differentiate equation for deformation and the double linear strain-hardening constitutive relation for bending moment against curvature are used in the analysis. The external work is assumed dissipated through the bending deformation of the legs and the crack propagation at the tip of the crack between the legs. A good agreement has been achieved between the theoretical predictions and the experimental results for the variation of external force with displacement. It has been found that the variation of bending force with displacement significantly depends on the strain-hardening modulus and the tearing force.