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# Showing papers in "Mechanics Based Design of Structures and Machines in 2014"

Journal ArticleDOI
TL;DR: In this article, the direct stiffness method is used to construct a stiffness model of the roller screw mechanism, which allows for a better understanding of the sensitivities of stiffness and contact stresses in the mechanism with various design parameters.
Abstract: In this paper, the direct stiffness method is used to construct a stiffness model of the roller screw mechanism. This method models the entire roller screw mechanism as a large spring system composed of individual springs representing the various compliances. In addition to predicting the overall stiffness of the mechanism, the direct stiffness method can calculate the distribution of load across the threads of the individual bodies. With the load on the individual threads known, the contact stresses can be calculated. This allows for a better understanding of the sensitivities of stiffness and contact stresses in the mechanism with various design parameters and can ultimately be used to design roller screws that are stiffer and with lower contact stresses.

58 citations

Journal ArticleDOI
, Pan Jin1
TL;DR: In this paper, the authors used the Hamilton's principle to derive the governing equations of motion for laminated shallow curved beams based on the trigonometric shear deformation theory in which the sinusoidal function is used in the displacement field in terms of the thickness coordinate to represent the deformation.
Abstract: Free vibration analysis of cross-ply laminated shallow curved beams is carried out by using the dynamic stiffness method. Hamilton's principle is adopted to derive the governing equations of motion for laminated shallow curved beams based on the trigonometric shear deformation theory in which the sinusoidal function is used in the displacement field in terms of the thickness coordinate to represent the shear deformation. The dynamic stiffness matrix is formulated directly from the exact solutions of the homogeneous governing differential equations. The application of the dynamic stiffness matrix is demonstrated by investigating the natural frequencies and mode shapes of the laminated shallow curved beams with various boundary conditions. The effects of stacking sequence, material orthotropy ratio, length to thickness ratio, and curvature ratio on the free vibration characteristics of the laminated shallow curved beams are studied. Compared to some available solutions in the literature, the numerical resul...

36 citations

Journal ArticleDOI
TL;DR: In this article, an exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load.
Abstract: This paper presents the dynamic response of uniform Timoshenko beams with arbitrary boundary conditions using Dynamic Green Function. An exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load. This technique is based on the Dynamic Green Function. The effect of different boundary conditions, load, and other parameters is assessed. Finally, some numerical examples are shown to illustrate the efficiency and simplicity of the new formulation based on the Dynamic Green Function.

29 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a new theoretical model and a problem-specific metaheuristic approach when the only source of uncertainty is the variability of the applied load directions, which is independent from the theoretical description of the uncertainty which may be either probabilistic (stochastic) or possibilistic (fuzzy).
Abstract: In the real-world truss optimization problems, the optimal performance obtained using conventional deterministic methods can be dramatically degraded in the presence of sources of uncertainty. The source of uncertainty may be the variability of applied loads, spatial positions of nodes, and section and material properties. In this paper, we present a new theoretical model and a problem-specific metaheuristic approach when the only source of uncertainty is the variability of the applied load directions. The essence of the novel conception is independent from the theoretical description of the uncertainty which may be either probabilistic (stochastic) or possibilistic (fuzzy). In the presented unified (nonprobabilistic and nonpossibilistic) approach, the varying load directions are handled as uncertain-but-bounded parameters. The result of the optimization is a robust minimal-weight truss design, which is invariant to the investigated load uncertainty type. The well-known ten-bar plane truss example with th...

26 citations

Journal ArticleDOI
TL;DR: In this article, the effect of random system properties is accounted to estimate the free vibration of multilayered composite shell panel in hygrothermal environment, and the analysis is carried out by using quadratic C0 eight-noded isoparametric element.
Abstract: In this article, the effect of random system properties is accounted to estimate the free vibration of multilayered composite shell panel in hygrothermal environment. The majority of previous investigations assumed that the material properties are independent of temperature and moisture. Establishing margin on material properties for design, analysis, and conceptualizing the material is highly difficult and uncertain. To perturb that, a first-order perturbation technique is adopted to obtain the response statistics of the structure by obtaining the mean and variance of random natural frequencies. The higher-order shear deformation theory with 9 degrees of freedom per node with the von-Karman sense of nonlinear kinematics is employed for generating basic formulation. The analysis is carried out by using quadratic C0 eight-noded isoparametric element. The governing equation for free vibration of laminated composite panel is derived using variational principle, which is a generalization of the principle of v...

24 citations

Journal ArticleDOI
TL;DR: In this article, an optimization of the infinitely variable transmission (IVT) was proposed to decrease the vehicle fuel consumption in a driving cycle, and the results showed that the vehicle FC of the vehicle equipped with the optimized IVT is approximately 7% and 4.7% compared to the cases of using the optimized six-speed and nine-speed manual transmissions, respectively.
Abstract: One solution to reduce fuel consumption (FC) of vehicles is to use infinitely variable transmission (IVT) as the power train. However, inappropriate design of IVT leads to an inadequate decrease in the vehicle FC. Therefore, in order to reach a maximum fuel economy, an optimization on the power train proves to be necessary. The present article aims to optimize IVT to decrease the vehicle FC in a driving cycle. The results have revealed that the FC of the vehicle equipped with the optimized IVT is approximately 7% and 4.7% compared to the cases of using the optimized six-speed and nine-speed manual transmissions, respectively.

24 citations

Journal ArticleDOI

TL;DR: In this paper, a wire actuated robot with articulated links like in a snake robot has been designed and developed for biopsy as an add-on to the current endoscope.
Abstract: In vivo robot is an emerging medical technology that could greatly help biopsy and surgery. This paper proposes to design and develop a miniature in vivo robot for biopsy as an add-on to the current endoscope. To allow more dexterity and flexibility, a four degree of freedom (DOF) robot manipulator is proposed. Accordingly, a wire actuated robot with articulated links like in a snake robot has been conceptualized. The robot was mathematically modeled and designed. To test the design, a 4-scaled aluminum model was manufactured. The kinematics of the model is verified experimentally. The four degree of freedom of the miniature robot are: a linear motion of the flexible shaft (first DOF); an axial rotation of the flexible shaft (second DOF); planar through differential wire movement (third DOF); and a combined wire motion for clipper action to take biopsy (fourth DOF). The proposed robot manipulator was modeled in SolidWorks and the kinematic and dynamic analysis was performed using the Robotics Toolbox in M...

23 citations

Journal ArticleDOI
TL;DR: In this paper, the authors apply the differential transformation method (DTM) to solve linear and nonlinear vibration problems of elastically end-restrained beams, which demonstrates many advantages such as rapid convergence, high accuracy, and computational stability.
Abstract: The objective of this paper is to apply the differential transformation method (DTM) to solve linear and nonlinear vibration problems of elastically end-restrained beams. The method demonstrates many advantages such as rapid convergence, high accuracy, and computational stability to determine linear and nonlinear natural frequencies as well as mode shapes of such beams. The mathematical models provided in this paper can be solved easily using symbolic tools in available software packages such as Maple and Matlab. An accuracy of the present solutions is confirmed by comparing with some published results in the open literature. New numerical results of nonlinear frequency ratio of beams supported by various types of elastic boundary conditions are presented and discussed in detail. The significant effects of translational and rotational springs including vibration amplitudes on linear and nonlinear vibration results are also taken into investigation. Based on the numerical exercises, it is revealed that the...

23 citations

Journal ArticleDOI
TL;DR: In this paper, a four-fingered micro gripper under the actuation of Ionic Polymer Metal Composite (IPMC) has been addressed, which can manipulate microobject less than 1mm diameter as well as macro object within the diameter of 10mm.
Abstract: Over the past few decades, the Electro Active Polymer (EAPs) has become quite useful for vast applications in the field of robotic and bio-mimetic. Ionic Polymer Metal Composite (IPMC) is one of the EAPs which holds an excellent bending property at low actuation voltage resulting high force output; thus, it is capable of doing work as good as human finger tip when the same is employed as an actuator for micromanipulation. In the present investigation, a four-fingered micro gripper under the actuation of IPMC has been addressed. The microgripper consists of four fingers made of Polydimethyl Siloxane and each finger has three notches. The novelty of this gripping device is in its multifunction operation. It can manipulate microobject less than 1 mm diameter as well as macro object within the diameter of 10 mm. This finger design is compliant in nature. The development of micropart handling devices and allied research is a highly challenging task. The principle on which the gripper operates and its fabricati...

23 citations

Journal ArticleDOI
TL;DR: In this paper, a finite elements model of an adaptive composite panel with embedded shape memory alloy actuators is presented, where a combination of shell, beam and link elements are employed to model the panel.
Abstract: This article focuses on the development of a finite elements model of an adaptive composite panel with embedded shape memory alloy actuators. It is firstly shown that a combination of shell, beam and link elements could be employed to model the panel. A simplified version of the Likhachev model is then employed as the constitutive relation for the actuators. Several experimental tests were successfully carried out on a prototype to validate the model and to demonstrate the possibility of controlling the panel shape. Further works should consider improving the technique employed for reading the actuators’ temperature during experimental tests.

22 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear constrained structural optimization is proposed for static damage detection of three-and two-dimensional frames based on the minimization of difference between the measured and analytical static displacements of frames.
Abstract: A new algorithm for static damage detection of three- and two-dimensional frames is presented in this paper. This approach is based on the minimization of difference between the measured and analytical static displacements of frames. The damage detection problem is solved as a nonlinear constrained structural optimization. In this strategy, the global structural stiffness matrix is parameterized. To achieve the goal, a new technique based on the eigen decomposition of the local elemental stiffness matrix is suggested. Structural damage is modeled as a reduction in cross-sectional properties of the elements. It is assumed that the stiffness matrix of the structure is perturbed due to damage. Hence, the damaged structural stiffness matrix is presumed to be the sum of the stiffness matrix of the undamaged structure and the perturbation matrix. Consequently, the sum of these matrices should be inverted in each iteration. Instead of the common ways of inversion, Sherman–Morrison–Woodbury formula is employed. P...

Journal ArticleDOI
, Feng Gao1, Q. J. Ge1
TL;DR: Based on the G F sets theory, the general form of number synthesis equations are presented, which predict the structure parameters of parallel mechanisms in the design process with the requirements of dimensions of the parallel mechanisms end-effectors characteristics, overconstraints, passive freedoms, redundant freedoms, and redundant actuation inputs.
Abstract: Type synthesis of parallel robotic mechanisms has drawn a lot of interest. In this paper, we treat one basic issue of this scientific problem: number synthesis. Based on the G F sets theory, the general form of number synthesis equations are presented, which predict the structure parameters of parallel mechanisms in the design process with the requirements of dimensions of the parallel mechanisms end-effectors characteristics, overconstraints, passive freedoms, redundant freedoms, and redundant actuation inputs. These requirements are described, respectively, and the uses of the number synthesis equations are illustrated through several examples. The number synthesis query table and programs are presented to provide a systematic method, whose simplicity and validity is illustrated by an example.

Journal ArticleDOI

TL;DR: In this article, a micro-newton static force sensor is presented as a packaged product, which consists of a compliant mechanism that amplifies the displacement caused by the force that is to be measured.
Abstract: A micro-newton static force sensor is presented here as a packaged product. The sensor, which is based on the mechanics of deformable objects, consists of a compliant mechanism that amplifies the displacement caused by the force that is to be measured. The output displacement, captured using a digital microscope and analyzed using image processing techniques, is used to calculate the force using precalibrated force-displacement curve. Images are scanned in real time at a frequency of 15 frames per second and sampled at around half the scanning frequency. The sensor was built, packaged, calibrated, and tested. It has simulated and measured stiffness values of 2.60N/m and 2.57N/m, respectively. The smallest force it can reliably measure in the presence of noise is about 2 mu N over a range of 1.4mN. The off-the-shelf digital microscope aside, all of its other components are purely mechanical; they are inexpensive and can be easily made using simple machines. Another highlight of the sensor is that its movable and delicate components are easily replaceable. The sensor can be used in aqueous environment as it does not use electric, magnetic, thermal, or any other fields. Currently, it can only measure static forces or forces that vary at less than 1Hz because its response time and bandwidth are limited by the speed of imaging with a camera. With a universal serial bus (USB) connection of its digital microscope, custom-developed graphical user interface (GUI), and related software, the sensor is fully developed as a readily usable product.

Journal ArticleDOI
TL;DR: In this article, a flexure hinge-based parallel manipulator is designed and optimally dimensioned using a finite element method (FEM) and empirical functions set up with the help of FEM.
Abstract: The operation of flexure hinge-based parallel manipulators primarily relies on their stiffness or compliance characteristics, which are considered by means of an analytical method, the finite element method (FEM) or an experimental method. A universal analytical method is adopted for flexure hinges. It is enhanced with empirical functions set up with the help of FEM. Results obtained analytically and with FEM are experimentally verified. General equations of stiffness and compliance calculation are given for flexure hinge-based parallel manipulators. On the basis of these mathematical models, a high-precision micro manipulator is monolithically designed and optimally dimensioned. Finally, a functional model is realized and preliminary tested.

Journal ArticleDOI

TL;DR: Carbon-infiltrated vertically aligned carbon nanotube (CNT) forests are fabricated into various designs of compliant cell restraint mechanisms, leading to a more effective design that meets the stated design requirements.
Abstract: Unique micromechanisms are required to grasp mouse egg cells while genetic material is inserted into the cell through micro or nanoinjection. To obtain the high aspect ratio needed to fully grasp the 100 μm-diameter cells, carbon-infiltrated vertically aligned carbon nanotube (CNT) forests are fabricated into various designs of compliant cell restraint mechanisms. Six preliminary designs are fabricated and tested, leading to a more effective design that meets the stated design requirements. This improved mechanism is discussed in detail. Finally, as a possible alternative to these more complicated mechanisms, a simple CNT passive cell restraint structure is also presented.

Journal ArticleDOI
TL;DR: The biomimetic behavior of an ionic polymer metal composite (IPMC) based artificial finger for micro robot which can be applicable in holding the object and an IPMC based micro gripper is demonstrated.
Abstract: This paper presents the biomimetic behavior of an ionic polymer metal composite (IPMC) based artificial finger for micro robot which can be applicable in holding the object. In this work, IPMC based artificial finger is actuated by controlled electromyographic (EMG) signal. The EMG signal is taken from human index finger via EMG sensor. This signal is pre-amplified before transferring to IPMC for achieving the large bending behavior of IPMC. The biomimetic actuation behavior of IPMC is studied by movement of index finger muscles through long tendons. The stability analysis of EMG signal from human index finger is carried out by providing the proportional–integral–derivative (PID) control system. Experimentally, it is observed that IPMC finger can hold the micro component when IPMC finger is activated through EMG via human muscles and an IPMC based micro gripper is demonstrated.

Journal ArticleDOI
TL;DR: In this paper, the authors present the theoretical concept and the practical implementation of square foot manufacturing (SFM) for micro manufacturing with modular, mutable, ad-hoc configurable, and function-integrated small machine tools.
Abstract: This article presents the theoretical concept and the practical implementation of Square Foot Manufacturing (SFM). The concept meets the demands for micro manufacturing with modular, mutable, ad-hoc configurable, and function-integrated small machine tools. Here, a feed unit, a measuring system, a workpiece clamping device, and mechanical interfaces are described as components of the machine tool system to prove the feasibility and advantages of the SFM concept. The feed unit uses the principles of a monolithic flexure-based mechanism combined with piezo stack actuators. High precision is guaranteed by avoiding positioning errors and friction of conventional guidance systems. A low-force clamping device uses an elastic deflection of its chuck to securely fasten micro workpieces. It also acts as a workpiece carrier allowing for various production layouts. The mechanical interfaces are based on a kinematic coupling to provide high repeat position accuracy. The interface is necessary to obtain the SFM-typica...

Journal ArticleDOI
TL;DR: In this article, an adaptive multidisciplinary optimization method is proposed for the lightweight optimization problem with weld fatigue constraints, where kriging surrogate models are used to replace the time-consuming computer simulations through the optimization procedure.
Abstract: As the speed of railway transportation grows rapidly, welded structures have been commonly used for the car bodies and bogies. Fatigue failure of a welded structure with fluctuating loads usually occurs at weld seams. And thus the fatigue strength of weld seams should be considered in the optimization of these structures. In this paper, an adaptive multidisciplinary optimization method is proposed for the lightweight optimization problem with weld fatigue constraints. The kriging surrogate models are used to replace the time-consuming computer simulations through the optimization procedure. The master S–N curve method in ASME standard is adopted for weld fatigue assessment due to its mesh-insensitivity and reliability. For a brake beam structure of a high-speed train, a lightweight optimization model with static strength and weld fatigue constraints is constructed and solved in light of the proposed optimization method. After optimization, the weight of the brake beam is reduced by 12.5% and the values of...

Journal ArticleDOI
TL;DR: In this paper, a small displacement analytical model is proposed for the out-of-plane compliances of symmetric notch flexure hinges with circular longitudinal axis and midpoint radial symmetry that function as monolithic joints in flexible mechanisms.
Abstract: A small-displacement analytical model is proposed for the out-of-plane compliances of notch flexure hinges with circular longitudinal axis and midpoint radial symmetry that function as monolithic joints in flexible mechanisms. The hinges are constructed from several serially connected segments with small and constant out-of-plane width, variable in-plane thickness, and are subjected to coupled bending and torsion. The six compliances of a symmetric notch hinge are obtained as linear combinations of compliances defining the segments that form one half of the full flexible hinge. The general analytical model is applied to the circular-axis, right circularly corner-filleted hinge design whose compliances are validated by finite element simulation. A comparison is performed between the out-of-plane and the in-plane compliances of this flexure hinge. The right circularly corner-filleted configuration is also compared to the circular-axis, constant-thickness flexure hinge with respect to the out-of-plane static...

Journal ArticleDOI
TL;DR: In this article, the meshless local Petrov-Galerkin method was used to analyze the cracked plate made of functionally graded material and the stress intensity factor of Mode I and II, maximum energy release rate and crack initiation angle were determined under the influence of various nonhomogeneity ratios, crack length, and material gradation angle.
Abstract: In this article, the meshless local Petrov–Galerkin method is used to analyze the cracked plate made of functionally graded material. The stress intensity factor of Mode I & II, maximum energy release rate and crack initiation angle are determined under the influence of various nonhomogeneity ratios, crack length, and material gradation angle. To solve discrete dynamic equations, a new effective method is extended and utilized. To find crack initiation angle, a simple and easy to use formula is suggested here. The edge-cracked functionally graded plate is considered under the uniform membrane and fixed grip conditions; also, the center-cracked functionally graded plate is analyzed under the uniform membrane and impact loads.

Journal ArticleDOI
TL;DR: In this paper, the NURBS tool path curve is realized in real time by mapping the feedrate with a cubic curve with respect to time satisfying the machine dynamics and chord error.
Abstract: This paper provides a suitable methodology to implement a high-performance and precise NURBS interpolator considering machine dynamics. The NURBS tool path curve is realized in real time by mapping the feedrate with a cubic curve with respect to time satisfying the machine dynamics and chord error. This is done by analyzing the feedrate profile offline and scheduling it with respect to time using a time optimal jerk limited algorithm. The proposed and the conventional NURBS interpolators are implemented in a three axis micro machine tool and the machining performance with respect to surface finish at different feedrates is compared. It is found that the feedrate profile obtained using the proposed interpolator scheme results in improved surface finish. Experimental evidences regarding the improvement in surface finish using a NURBS interpolator are shown for the first time according the authors knowledge. The proposed interpolator is designed with flexibility so that it can be implemented in all types of ...

Journal ArticleDOI
TL;DR: In this article, the steady-state vibrations in the neighborhood of resonance conditions of a rotor with 6 degrees of freedom in linear homogeneous elastoviscous field are analyzed and the analytical solution of the differential equations is implemented applying Bogoliubov-Mitropolski's asymptotics.
Abstract: The efforts directed toward ensuring long trouble-free operation of rotating machinery are in the focus of many scientific investigations. Electric power rotors and turbines, aircraft engines, automotive drive trains, kinetic energy storage systems are only few examples of machines that are to operate efficiently and safely. Very often they are imposed on external excitations, which are characterized by time-dependent characteristics and causing nonstationary random oscillations. In this paper, the dynamics of high-speed rotating rotor is analytically and numerically analyzed. The analytical investigations studied the steady-state vibrations in the neighborhood of resonance conditions of a rotor with 6 degrees of freedom in linear homogeneous elastoviscous field. Unstable frequencies zones are determined by “limited” power of an electric motor with linear characteristic and only one time constant. The analytical solution of the differential equations is implemented applying Bogoliubov–Mitropolski's asympt...

Journal ArticleDOI
TL;DR: In this paper, a Displacement-amplifying Compliant Mechanism (DaCM) is used to match the stiffness of the suspension so that there is substantial net amplification without compromising the bandwidth.
Abstract: With the premise that electronic noise dominates mechanical noise in micromachined accelerometers, we present here a method to enhance the sensitivity and resolution at kHz bandwidth using mechanical amplification. This is achieved by means of a Displacement-amplifying Compliant Mechanism (DaCM) that is appended to the usual sensing element comprising a proof-mass and a suspension. Differential comb-drive arrangement is used for capacitive-sensing. The DaCM is designed to match the stiffness of the suspension so that there is substantial net amplification without compromising the bandwidth. A spring-mass-lever model is used to estimate the lumped parameters of the system. A DaCM-aided accelerometer and another without a DaCM-both occupying the same footprint-are compared to show that the former gives enhanced sensitivity: 8.7 nm/g vs. 1.4 nm/g displacement at the sensing-combs under static conditions. A prototype of the DaCM-aided micromachined acclerometer was fabricated using bulk-micromachining. It was tested at the die-level and then packaged on a printed circuit board with an off-the-shelf integrated chip for measuring change in capacitance. Under dynamic conditions, the measured amplification factor at the output of the DaCM was observed to be about 11 times larger than the displacement of the proof-mass and thus validating the concept of enhancing the sensitivity of accelerometers using mechanical amplifiers. The measured first in-plane natural frequency of the fabricated accelerometer was 6.25 kHz. The packaged accelerometer with the DaCM was measured to have 26.7 mV/g sensitivity at 40 Hz.

Journal ArticleDOI
TL;DR: In this article, the basic mechanism of soldier fly halteres is presented to demonstrate its use as a vibratory gyroscope and a static force sensor is used to determine the stiffness of the haltere shaft.
Abstract: Dipteran insects are known to receive mechanosensory feedback on their aerial rotations from a pair of vibratory gyroscopic organs called halteres. Halteres are simple cantilever-like structures with an end mass that evolved from the hind wings of the ancestral four-winged insects form. In most Diptera, including the soldier fly Hermetia illucens, the halteres vibrate at the same frequency as the wings. These vibrations occur in a vertical plane such that any rotation about this plane imposes orthogonal Coriolis forces on the halteres causing their plane of vibration to shift laterally by a small degree. This motion results in strain variation at the base of the haltere shaft, which is sensed by the campaniform sensilla. This strain variation is, therefore, a key parameter for sensing body rotations. In this paper, we present a study of the basic mechanism of soldier fly halteres to demonstrate its use as a vibratory gyroscope. First, we use a static force sensor to determine the stiffness of the haltere,...

Journal ArticleDOI
TL;DR: In this article, the Lagrangian formalism in mechanics and genetic algorithms were used respectively as analyzer and optimizer for the kinematics optimization of the mechanical scissor systems of tipping.
Abstract: This paper investigates the kinematics optimization of the mechanical scissor systems of tipping. Lagrangian formalism in mechanics and genetic algorithms (GAs) are used respectively as analyzer and optimizer. Thus, multiobjective functions are considered and based on the reaction force of the hydraulic cylinder and the size of the whole mechanical system to obtain a final optimum one, more resistant and lighter. Two kinds of kinematics are optimized: a classical one which is usually adopted in industry and a suggested one including modifications. All optimized results are compared to the original one to demonstrate the effectiveness of the proposed methodology.

Journal ArticleDOI
TL;DR: In this paper, an efficient and accurate frame element for small-strain but large-displacement/rotation analyses of elastic planar frames is presented, based on the unification of the corotational concept and the Euler-Bernoulli-von Karman beam theory.
Abstract: This article presents an efficient and accurate frame element for small-strain but large-displacement/rotation analyses of elastic planar frames. The element formulation is based on the unification of the corotational concept and the Euler-Bernoulli-von Karman beam theory. The Hellinger-Reissner mixed functional is used to construct the locking-free Euler-Bernoulli-von Karman frame element. The directional derivative operator is used to linearize the Hellinger-Reissner mixed functional, thus resulting in the incremental element equations. The derived element stiffness matrix is symmetric and variationally consistent. The standard displacement interpolation functions for a linear frame element are used. With these assumed displacements, the force interpolation functions are derived such that the equilibrium equations in the deformed configuration are strictly satisfied. In the present study, the distributed loads along the element are assumed to be absent and only initially straight prismatic beams are con...

Journal ArticleDOI
TL;DR: In this article, the problem of optimal structural design with incomplete data concerning applied external loads is formulated as a multi-objective optimization problem and investigated analytically with the help of two principally different approaches: Nash-approach and Pareto-approaches.
Abstract: The study deals with the problems of optimal structural design with incomplete data concerning applied external loads The max(guaranteed) approach, based on worst case scenario, is used to take into account these uncertainties All considered problems are formulated as multiobjective optimization problems Investigation of the problems of minimization or maximization of vector-criteria is performed analytically with the help of two principally different approaches: Nash-approach and Pareto-approach Comparison of the procedures of analytical solutions shows the advantages and disadvantages of both approaches In particular, it was shown that in some shape optimization problems Pareto- and Nash-fronts, containing all optimal solutions of multiobjective optimization problems, are coincident

Journal ArticleDOI
Zi Ying Wu
TL;DR: In this paper, a pinned-pinned beam with one end fixed and the other end free to slide horizontally is considered and the relationship between the equivalent viscous damping and the relative vibration amplitude ratio is obtained by using the moving autoregressive model (MARM) method.
Abstract: A pinned–pinned beam with one end fixed and the other end free to slide horizontally is studied. Dry friction damping is modeled at the support boundaries of the beam. In order to analyze the variation of the equivalent viscous damping caused by the presliding friction, the LuGre friction model is employed. The relationship between the equivalent viscous damping and the relative vibration amplitude ratio is obtained by using the moving autoregressive model (MARM) method. The equivalent viscous damping caused by both sliding and the presliding friction is obtained by numerical simulation.

Journal ArticleDOI
TL;DR: In this article, the problem of estimation of some integral characteristics (functionals) is considered for anisotropic body constituting of the locally orthotropic material, where an orientation of the principal axes of orthotropy is not known beforehand at each point of the body and can be distributed by various ways in different parts of body including chaotic orientation.
Abstract: The problem of estimation of some integral characteristics (functionals) is considered for anisotropic body constituting of the locally orthotropic material. It is assumed that an orientation of the principal axes of orthotropy is not known beforehand at each point of the body and can be distributed by various ways in different parts of the body including chaotic orientation. The estimation of the upper and lower bounds of the considered integral characteristics is of principal importance and is based on the solution of the optimization problems and finding an extremal internal material structures which realize minimum and maximum of the functionals. This approach is applied in this article to some estimation problems of the heat conductivity and the torsion of elastic bars.

Journal ArticleDOI
TL;DR: In this article, a procedure for calculating relative accelerations in spatial mechanisms is extended to include ball joints, and the relationship of the relative velocities in a closed-loop mechanism is differentiated and then manipulated into set of simultaneous linear equations in the unknown relative acceleration.
Abstract: A procedure for calculating relative accelerations in spatial mechanisms is extended to include ball joints. The relationship of the relative velocities in a closed-loop mechanism is differentiated and then manipulated into set of simultaneous linear equations in the unknown relative accelerations. The derivatives of the joint-link modeling matrices, which are required to construct the vector of constants in this set of simultaneous linear equations, are formulated in terms of partial-derivative operator matrices to facilitate automatic differentiation in computer calculations. The joint-link modeling matrices, the relative velocities, and the relative accelerations are written in terms of dual numbers so to provide compact expressions which can be readily coded in object-oriented programming. The relationship of the calculated relative-acceleration components, which are expressed in the same coordinate frame, and the physical relative-acceleration components, which are naturally expressed in different co...