Showing papers in "Mechanics Based Design of Structures and Machines in 2017"

Enhanced whale optimization algorithm for sizing optimization of skeletal structures

Abstract: The whale optimization algorithm (WOA) is a recently developed swarm-based optimization algorithm inspired by the hunting behavior of humpback whales. This study attempts to enhance the original formulation of the WOA in order to improve solution accuracy, reliability and convergence speed. The new method, called enhanced whale optimization algorithm (EWOA), is tested in sizing optimization problems of truss and frame structures. The EWOA is compared with WOA and other metaheuristic methods developed in literature in four optimization problems of skeletal structures. Numerical results demonstrate the efficiency of the EWOA and WOA with the former algorithm being more efficient than its standard version.

Nonlocal Thermo-Electro-Mechanical coupling vibrations of axially moving piezoelectric nanobeams

Abstract: This work is concerned with the thermo-electro-mechanical coupling transverse vibrations of axially moving piezoelectric nanobeams which reveal potential applications in self-powered components of biomedical nano-robot. The nonlocal theory and Euler piezoelectric beam model are employed to develop the governing partial differential equations of the mathematical model for axially moving piezoelectric nanobeams. The natural frequencies of nanobeams under simply supported and fully clamped boundary constraints are numerically determined based on the eigenvalue method. Subsequently, some detailed parametric studies are presented and it is shown that the nonlocal nanoscale effect and axial motion effect contribute to reduce the bending rigidity of axially moving piezoelectric nanobeam and hence its natural frequency decreases within the framework of nonlocal elasticity. Moreover, the natural frequency decreases with increasing the positive external voltage, axial compressive force and change of temperature, while increases with increasing the axial tensile force. The critical speed and critical axial compressive force are determined and the dynamical buckling behaviors of axially moving piezoelectric nanobeams are indicated. It is concluded the nonlocal nanoscale parameter plays a remarkable role in the size-dependent natural frequency, critical speed and critical axial compressive force.

Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model

Abstract: The present paper is aimed at studying the effect of initial stress and the magnetic field on thermoelastic interactions in an isotropic, thermally and electrically conducting half-space whose surface is subjected to mechanical and thermal loads. The formulation is applied under the thermoelasticity theory with three-phase-lag, proposed by Choudhuri (2007). The normal mode analysis is used to obtain the expressions for the variables considered. Numerical and computations are performed for a specific material and the results obtained are represented graphically. Comparisons are made with the results predicted by different theories Lord–Shulman theory (L–S), the theory of thermoelasticity type III (G-N III) and the three-phase-lag model (3PHL) in the absence and presence of the initial stress and magnetic field.

Accurate dynamic analysis of functionally graded beams under a moving point load

Abstract: Based on the physical neutral surface, an N-node novel weak form quadrature beam element is proposed and the explicit formulas for computing the stiffness and mass matrices are given. The proposed element is then used to analyze the dynamic behavior of the functionally graded material (FGM) beams under a moving point load. Both elasticity modulus and mass density vary exponentially across the thickness. Investigations show that the maximum dynamic magnification factors are independent of the power-law exponent k at a fixed nondimensional parameter α. This finding may be useful in design and engineering applications.

On the size-dependent flexural vibration characteristics of unbalanced couple stress-based micro-spinning beams

Abstract: On the basis of the modified couple stress theory, some analytical results are obtained for vibrational parameters of micro-spinning Rayleigh beams with an axial mass-eccentricity distribution. The...

A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method

Abstract: A multi-objective optimization method for uncertain structures is developed based on nonlinear interval number programming (NINP) method. The NINP method is employed to transform each uncertain objective function into a deterministic single-objective optimization problem. Using the constraint penalty function method, a deterministic multi-objective and non-constraint optimization problem is formulated in terms of penalty functions. Then the micro multi-objective genetic algorithm and the intergeneration projection genetic algorithm are adopted as outer layer and inner optimization operator to solve the nesting optimization problem, respectively. Finally, four numerical examples are provided to demonstrate the effectiveness of the present method.

An efficient response identification strategy for nonlinear structures subject to nonstationary generated seismic excitations

Abstract: The Monte Carlo method is computationally demanding. Consequently, applying that method to high-dimensional nonlinear systems is practically not feasible. Therefore, a new strategy is proposed in this article, which enables the evaluation of the response statistics of high-dimensional structures subject to random seismic excitations in a nonlinear reduced low-order subspace. It is shown that the new model order reduction method provides the possibility to overcome the computational issue of large-scale Monte Carlo simulations. It provides reliable approximations of the response statistics, when compared with those of the non-reduced Monte Carlo method.

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

Abstract: The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically comput...

Optimized cross-spring pivot configurations with minimized parasitic shifts and stiffness variations investigated via nonlinear FEA

Abstract: Compliant mechanisms are nowadays a well-established means of achieving ultra-high precision, albeit at the expense of complex kinematics with the presence of parasitic motions. Diverse design configurations of compliant rotational joints called cross-spring pivots are hence studied in this work by applying various analytical and numerical approaches. Depending on the required precision and loading conditions, the limits of applicability of the available analysis tools, validated with nonlinear finite element calculations tuned with experimental data reported in literature, are established. The variation of design parameters allows, in turn, establishing design configurations of the studied mechanism that allow attaining minimized parasitic shifts and slight variations of its rotational stiffness, even when a broad range of rotations and varying transversal loads are considered, creating thus the preconditions for their application in high-precision micropositioning applications.

Free vibration of a thermoelastic hollow cylinder under two-temperature generalized thermoelastic theory

Abstract: The aim of this article is to study the exact solution for a free vibration in a thermoelastic hollow cylinder, which is initially undeformed and at uniform temperature. The formulation is applied in the context of two-temperature Green and Naghdi (2TGNIII) theory. Both the inner and outer curved surfaces of the cylinder are considered stress free and isothermal surfaces. The exact analytic solutions are obtained with the use of eigenvalue approach. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow cylinder are derived in a compact form. The validation of the roots for the dispersion relation are presented. The numerical results of natural frequency, thermoelastic damping and frequency shift of vibrations have been presented graphically.

Equivalent uniaxial accelerogram for CSS-based isolation systems assessment under two-components seismic events

Abstract: Concave surface slider (CSS) devices represent an effective solution for base-isolation design problems. In such isolators the energy dissipation capability is induced by the sliding motions which occur at one or more sliding interfaces. The spherical shape of the sliding surfaces provides a significant recentering behavior, by means of the stepwise projection of the applied vertical load with respect to both horizontal directions. For two-components earthquake excitations, the recentering force is computed as a linear spring with respect to displacements along the main directions of motion; whereas, the frictional response is returned by the stepwise projection of the total frictional force, which is aligned with respect to the trajectory of the device: thus, a bi-axial interaction of the directions of motion has to be accounted for, when a friction-based device is modelled. However, available commercial software which can capture such a behavior are limited. In this work an analytical procedure is defined, for the computation of an “equivalent uniaxial accelerogram” for the seismic assessment of a base-isolated structure, subjected to a bi-directional earthquake. Thanks to the proposed theory, it is possible to compute a single ground acceleration time-history, related to a proper direction angle, which can reproduce the same effects of a two-components seismic event on a base-isolated structural system: the analogy between the equivalent uniaxial and the bi-directional events has been studied in terms of acceleration, velocity and displacement spectra respectively. Results for the base-isolated structure have been analyzed in terms of displacement, absolute acceleration and interstorey shear responses.

Design of a curved surface constant force mechanism

Abstract: A new curved surface constant force mechanism which mainly consists of a roller and a curved surface has been proposed. The magnitude and the direction of normal force caused by squeezing between the roller and the curved surface satisfy a certain relationship, thus the decomposed force of the normal force keeps constant in a certain direction all the times. According to the envelope theorem, the trajectory of the roller center and the profile of the curved surface are obtained by ignoring friction. Then, the influence of the friction is discussed in detail. In addition, the simulation is performed to verify the theoretical calculation. The simulation results show that the output force is relatively constant and the friction has little effect on the output force.

Design of multi-degree motion haptic mechanisms using smart fluid-based devices

Abstract: This article presents two different types of haptic masters capable of 4-degree- of-freedom (DOF) force feedback utilizing magnetorheological fluid (MR) and electrorheological (ER) fluid. The proposed ER master consists of a spherical joint for 3-DOF rotational motion and a linear device for 1-DOF translational motion, the MR haptic master consists bi-directional clutches associated with a planetary gear system and one-directional clutch with a bevel gear system. After showing the configuration of each haptic mechanism, the torque and force models of the actuators are derived based on the field-dependent Bingham model. After undertaking optimal design with spatial limitation and desired torque level, two different types of haptic master systems are manufactured. The torque and force responses are experimentally evaluated to validate practical feasibility of the proposed haptic masters for medical application.

An index 0 differential-algebraic equation formulation for multibody dynamics: Nonholonomic constraints

Abstract: A method is presented for formulating and numerically integrating index 0 differential-algebraic equations of motion for multibody systems with holonomic and nonholonomic constraints Tangent space coordinates are defined in configuration and velocity spaces as independent generalized coordinates that serve as state variables in the formulation Orthogonal dependent coordinates and velocities are used to enforce position, velocity, and acceleration constraints to within specified error tolerances Explicit and implicit numerical integration algorithms are presented and used in solution of three examples: one planar and two spatial Numerical results verify that accurate results are obtained, satisfying all three forms of kinematic constraint to within error tolerances embedded in the formulation

A study of the hydraulically interconnected inerter-spring-damper suspension system

Abstract: A new hydraulically interconnected inerter-spring-damper suspension (HIISDS) is developed to compensate for traditional passive suspension limitations, such as the imbalance of ride performance and handling stability In this article, the structure and mechanism of the HIISDS system is briefly introduced at first, and compiled with hydraulically interconnected suspension (HIS) mode and hydraulic inerter-spring-damper (ISD) suspension mode A vehicle dynamic model of HIISDS system is then derived through these two suspension modes by using Matlab/Simulink Two different road excitations are used to validate the adaption of the two suspension modes The effectiveness of HIISDS has been verified by simulation results, in which vehicle ride comfort and handling stability are effectively coordinated through the HIISDS model switch Finally, an HIISDS suspension prototype is designed based on Simulink results, and test results reconfirm the partial performances of HIISDS modes effectively

Optimal synthesis and kinematic analysis of adjustable four-bar linkages to generate filleted rectangular paths

Abstract: Continuous and precise path generation of filleted-rectangle using adjustable four-bar mechanism is presented. Coupler path passing through precision points is verified using reconstructed adjustable parameter curve (RAPC) method proposed in this article. This method extracts adjustable parameter values of intermediate path points, along the filleted rectangular path generation profile, corresponding to uniformly incremented crank input values without using interpolation of data points. Influence of number of precision points and spacing between them in achieving perfect coupler path of filleted-rectangle are analyzed. Verification of filleted-rectangle path generation and kinematic analysis of adjustable four-bar crank-rocker mechanism are carried out through motion simulation. Hybrid method combining Genetic Algorithm and Pattern Search is used in the synthesis of adjustable four-bar mechanisms to generate coupler path for three different filleted-rectangles. Results and conclusions prove the va...

Nanometric positioning accuracy in the presence of presliding and sliding friction: Modelling, identification and compensation

Abstract: Presliding and sliding frictional effects, limiting the performances of ultrahigh precision mechatronics devices, are studied in this work. The state-of-the-art related to frictional behavior in both motion regimes is, hence, considered, and the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances present in a micromanipulation device. All the parameters of the model are identified via experimental set-ups and included in the overall MATLAB/SIMULINK model. With the aim of compensating frictional effects, the modelled response of the system is thus compared to experimental results when using proportional-integral-derivative (PID) control, feed-forward model-based compensation and a self-tuning adaptive regulator. The adaptive regulator proves to be the most efficient and is, hence, used in the final repetitive point-to-point positioning tests allowing to achieve nanometric precision and accuracy.

Elastic-plastic secondary indeterminate problem for thin-walled pipe through the inner-wall loading by three-point bending

Abstract: The inner-wall loading by three-point bending about thin-walled pipe is an elastic-plastic secondary indeterminate problem in the symmetrical three-roller setting round process. In this study, the shifting of the tangent point between the pipe and lower roller is ignored. The bilinear hardening material model is adopted, and the static equilibrium condition, physical relationship of elastic-plastic deformation, and deformation compatibility condition are taken into account. Based on the geometrical discrete idea, a semi-circular pipe is meshed equably into N micro-pipe-wall elements with same geometric parameters along the circumferential direction. Deformation characteristics of each element are calculated, and then the deformation history response of the whole pipe is resolved by the load increment method. The finite element model of static bending in three-roller setting round process is established by using the software package ABAQUS. The theoretical and simulated results show that the cross ...

Nonlinear dynamic behavior of base-isolated buildings with the friction pendulum system subjected to near-fault earthquakes

Abstract: In spite of the fact that avant-garde sliding bearings have been proposed, the application of the single friction pendulum (FP) bearing is increasing due to its conceptual simplicity; yet there are still important aspects of its behaviour that need further attention. More specifically, the FP system presents spatial variation of friction coefficient, depending on the sliding velocity of the FP bearings. Moreover, the frictional force and restoring stiffness during the sliding phase are proportional to the axial load. Long duration intense velocity pulses in the horizontal direction and high values of the ratio between vertical and horizontal peak ground acceleration are expected for near-fault earthquakes. Torsion with residual displacement and uplift of the FP system need to be better understood for base-isolated structures located in near-fault areas. To this end, a numerical investigation is carried out with reference to a six-storey reinforced concrete (r.c.) framed building, characterized by an...

An efficient explicit framework for determining the lowest structural buckling load using Dynamic Relaxation method

Abstract: This paper develops an efficient explicit algorithm for calculating buckling load of structures. Here, the modified Dynamic Relaxation method is utilized so that the first structural buckling load is...

Weakest link concept for springs fatigue

Abstract: In the present manuscript, a new approach is developed to account the stress gradient effect on fatigue life of springs. The new formula of crack growths per cycle is introduced. The expressions for spring length over the number of cycles are derived in terms of higher transcendental function. The closed-form solutions are used for the estimation of the fatigue life of heterogeneously stressed structural members. The probability distribution of the fatigue limit for heterogeneously stressed structural elements is evaluated. The proposed approach for the stress gradient sensitivity of fatigue life is based on the weakest link concept. The weakest link approach is applied to calculate the number of cycles to crack initiation of structural elements under different probability levels. The effect of stress ratio on elongation of crack is discussed. The developed theory is applied to helical springs under cyclic load. The fatigue sensitivity to stress concentration is addressed in application to springs...

Automatic calibration process for optimal control of clutch engagement during launch

Abstract: Launching a vehicle is related to changing acceleration High acceleration is desired for sporty driving behavior, however, jerk as change of acceleration and change of jerk are major sources of discomfort Modern double-clutch transmissions allow to shape the acceleration transition by controlling the torque transmitted by the clutch, which is why the question arises about an optimal transition law for the acceleration and optimal calibration of automatic transmissions A bi-criterion optimization problem is formulated to account for both sportiness and comfort, where the latter criterion is defined as deviation from an ideal acceleration transition For finding such an optimal transition, another tri-criterion optimization problem is set up and solved analytically The calibration of the transmission TCU is then performed in a SIL (Software-in-the-Loop) environment where results demonstrate the validity of the proposed approach

Truss topology optimization under uncertain nodal locations with proportional topology optimization method

Abstract: This paper presents an approach to solving truss topology optimization problem with small uncertainty in the locations of the structural nodes. The nodal locations in the truss are assumed to be random, and the probabilistic method is used here to deal with the uncertainty. The objective of the optimization problem is to minimize the mean compliance of the truss structure under nodal location uncertainty. It is a well-acknowledged barrier to compute the inverse of the structural stiffness matrix which involves variations in the optimization problem. In this paper, based on Neumann series expansion, this optimization problem can be recast into a simpler deterministic structural optimization problem. In order to avoid the sensitivity calculations for the objective function, the proportional topology optimization method which shows comparable efficiency and accuracy with gradient-based method is used. The numerical examples demonstrate the effectiveness and high efficiency of the proposed approach, and f...

A chassis-based kinematic formulation for flexible multi-body vehicle dynamics

Abstract: This research proposed an efficient implicit integration method for the real-time simulation of flexible multi-body vehicle dynamics models. The equations of motion for the flexible bodies were formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. The proposed approach does not require evaluation of system Jacobian and its LU-decomposition in time loof of simulation. This is one of the key aspects that enable high computational efficiency of the proposed method. The numerical simulation results of the proposed approach were matched up with those of the conventional approach but the computation time can be reduced by applying the proposed method. The joint constraint and generalized force equations are the same as the equations for rigid vehicle dynamics models because the joints and forces between flexible bodies are connected by the RBE (rigid body element). On the various driving conditions, the numerical simulation results show that th...

A mesh free method using rectangular pre-solved domains using Kronecker products

Abstract: In this paper, a mesh free algorithm using large pre-solved domain is developed. Using the largest rectangle inside an arbitrary domain, a pre-solved rectangular domain is established using Kronecker product and graph theory rules. This pre-solved domain is efficiently inserted into the mesh free formulation of partial differential equations (PDEs) and engineering problems to reduce the computational complexity and execution time of the solution. The general solution of the pre-solved rectangular domain is formulated for second-order shape functions. The efficiency of the present algorithm depends on the relative size of the large rectangular domain and the main domain; however, the method remains as efficient as a standard method for even small relative sizes. For adaptive procedures with nonuniform density of distributed points in the domain, smaller (e.g. sub-maximal) rectangular domain can be used. The application of the method is demonstrated using some examples.

Fracture analysis on a layered multiferroic smart structure containing non-periodic interfacial cracks under magnetic/electric and mechanical loadings

Abstract: The problems of periodic cracks have been widely solved in existing literature of fracture mechanics. Although the assumption of periodicity facilitates the theoretical derivation, practical multiple cracks in most cases are not periodically distributed in materials and structures. The present article performs fracture analysis on a piezoelectric/piezomagnetic/piezoelectric (PE/PM/PE) tri-layered smart structure containing nonperiodic interfacial cracks under magnetic/electric and mechanical loadings. The methods of dislocation simulation, Green's function and Cauchy singular integral equations are employed to solve the problem. Stress intensity factors (SIFs) are numerically calculated, and parametric studies are conducted to demonstrate the variation laws of SIFs versus geometrical parameters. The obtained conclusions may provide references for the optimal design of PE/PM/PE smart structures.

Motion generation of RCCC mechanism using numerical atlas

Abstract: This article presents a synthesis method for the motion generation of RCCC mechanism using the numerical atlas. Based on the Fourier series theory, the geometrical model of the rigid body rotation angle of RCCC mechanism is established. Through harmonic analysis, the rotation angle output characteristics were observed to be dependent on the rigid body rotation angle operator. Subsequently, two numerical atlas databases are constructed. The theoretical formulas to calculate the real size and installing dimensions were proposed. On the basis of the theoretical formulas and two numerical atlas databases, the problem of rigid body guided synthesis of RCCC is solved.

Dynamic characteristics and frequency response function for frame with dampers with uncertain design parameters

Abstract: The influence of uncertain design parameters on dynamic characteristics and the frequency response function is considered in this paper. A structure with dampers modeled as a shear frame is analyzed. The dampers properties of dampers are described by fractional derivatives. The design parameters of the considered structure change only in a specified range and the interval analysis is taken into account in calculating the lower and upper bounds of dynamic characteristics. Several methods are used to obtain the limit values of objective functions: the vertex method and the method of approximation using the first- and the second-order Taylor series expansion. The vertex method is adopted as a comparative method. Two examples are presented in order to illustrate the considered methods. In the case of large uncertainties, the obtained results differ from those obtained by means of the vertex method. Therefore, a new method using the second-order Taylor series expansion is proposed. The method consists ...

Some exact analytical solutions in structural optimization

Abstract: In this article, the isoperimetric inequalities arising in exactly solvable structural optimization problems of stability are discussed. The purpose of this article is to review some types of inequalities that may be regarded as “isoperimetric.” This type of inequalities is long known in geometry and physics; see, e.g., Polya and Szego (1951), Banichuk (1977), Bandle (1980), and Chavel (2001). The variational method is a powerful way to prove inequalities for systems described by ordinary differential equations. The proof of isoperimetric inequalities exploits the variational method and the Holder inequality. The applications of this method for stability problems are illustrated in this article. The inequalities for Euler's column with boundary conditions of mixed type, for a twisted rod with periodic simple supports, and for a ring acted upon by a uniformly distributed, compressive hydrostatic load are rigorously verified.

Modified Parker-Sochacki method for solving nonlinear oscillators

Abstract: A new approach is presented for solving nonlinear oscillatory systems. Parker-Sochacki method (PSM) is combined with Laplace-Pade resummation method to obtain approximate periodic solutions for three nonlinear oscillators. The first one is Duffing oscillator with quintic nonlinearity which has odd nonlinearity. The second one is Helmholtz oscillator which has even nonlinearity. The last one is a strongly nonlinear oscillator, namely; relativistic harmonic oscillator which has a fractional order nonlinearity. Solutions are also obtained using Runge-Kutta numerical method (RKM) and Lindstedt-Poincare method (LPM). However, the LPM could not be used to solve the relativistic harmonic oscillator since it is a strongly nonlinear oscillator. The comparison between these solutions shows that the convergence zone for the Parker-Sochacki with Laplace-Pade method (PSLPM) is remarkably increased compared to PSM method. It also shows that the PSLPM solutions are in excellent agreement with LPM solutions for D...