Search results for: Nonlinear Static Analysis.

Authors: R. I. Liban, N. Tayşi

Abstract:

This paper deals with a nonlinear finite element analysis to examine the behavior up to failure of cantilever composite steel-concrete beams which are prestressed externally. 'Pre-' means stressing the high strength external tendons in the steel beam section before the concrete slab is added. The composite beam contains a concrete slab which is connected together with steel I-beam by means of perfect shear connectors between the concrete slab and the steel beam which is subjected to static loading. A finite element analysis will be done to study the effects of external prestressed tendons on the composite steel-concrete beams by locating the tendons in different locations (profiles). ANSYS version 12.1 computer program is being used to analyze the represented three-dimensional model of the cantilever composite beam. This model gives all these outputs, mainly load-displacement behavior of the cantilever end and in the middle span of the simple support part.

Keywords: Composite steel-concrete beams, external prestressing, finite element analysis, ANSYS.

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Authors: Mohamed M. El-Gendy, Ibrahim A. El-Arabi, Rafik W. Abdel-Missih, Omar A. Kandil

Abstract:

In the present research, a finite element model is presented to study the geometrical and material nonlinear behavior of reinforced concrete plane frames considering soil-structure interaction. The nonlinear behaviors of concrete and reinforcing steel are considered both in compression and tension up to failure. The model takes account also for the number, diameter, and distribution of rebar along every cross section. Soil behavior is taken into consideration using four different models; namely: linear-, nonlinear Winkler's model, and linear-, nonlinear continuum model. A computer program (NARC) is specially developed in order to perform the analysis. The results achieved by the present model show good agreement with both theoretical and experimental published literature. The nonlinear behavior of a rectangular frame resting on soft soil up to failure using the proposed model is introduced for demonstration.

Keywords: Nonlinear analysis, Geometric nonlinearity, Material nonlinearity, Reinforced concrete, Finite element method, Soilstructure interaction, Winkler's soil model, Continuum soil model

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: Alok Madan, Ashok Gupta, Arshad K. Hashmi

Abstract:

Non-linear dynamic time history analysis is considered as the most advanced and comprehensive analytical method for evaluating the seismic response and performance of multi-degree-of-freedom building structures under the influence of earthquake ground motions. However, effective and accurate application of the method requires the implementation of advanced hysteretic constitutive models of the various structural components including masonry infill panels. Sophisticated computational research tools that incorporate realistic hysteresis models for non-linear dynamic time-history analysis are not popular among the professional engineers as they are not only difficult to access but also complex and time-consuming to use. In addition, commercial computer programs for structural analysis and design that are acceptable to practicing engineers do not generally integrate advanced hysteretic models which can accurately simulate the hysteresis behavior of structural elements with a realistic representation of strength degradation, stiffness deterioration, energy dissipation and ‘pinching’ under cyclic load reversals in the inelastic range of behavior. In this scenario, push-over or non-linear static analysis methods have gained significant popularity, as they can be employed to assess the seismic performance of building structures while avoiding the complexities and difficulties associated with non-linear dynamic time-history analysis. “Push-over” or non-linear static analysis offers a practical and efficient alternative to non-linear dynamic time-history analysis for rationally evaluating the seismic demands. The present paper is based on the analytical investigation of the effect of distribution of masonry infill panels over the elevation of planar masonry infilled reinforced concrete [R/C] frames on the seismic demands using the capacity spectrum procedures implementing nonlinear static analysis [pushover analysis] in conjunction with the response spectrum concept. An important objective of the present study is to numerically evaluate the adequacy of the capacity spectrum method using pushover analysis for performance based design of masonry infilled R/C frames for near-field earthquake ground motions.

Keywords: Nonlinear analysis, capacity spectrum method, response spectrum, seismic demand, near-field earthquakes.

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Authors: K. Abuzayan, H. Alabed, J. Ezarrugh, M. Agila

Abstract:

Static and dynamic balance are essential in daily and sports life. Many factors have been identified as influencing static balance control. Therefore, the aim of this study was to apply the (XCoM) method and other relevant variables (CoP, CoM, F_h, KE, P, Q, and, AI) to investigate sport related activities such as hopping and jumping. Many studies have represented the CoP data without mentioning its accuracy so several experiments were done to establish the agreement between the CoP and the projected CoM in a static condition. 5 healthy male were participated in this study (Mean ± SD:- age 24.6 years ±4.5, height 177cm ± 6.3, body mass 72.8kg ± 6.6).Results found that the implementation of the XCoM method was found to be practical for evaluating both static and dynamic balance. The general findings were that the CoP, the CoM, the XCoM, F_h, and Q were more informative than the other variables (e.g. KE, P, and AI) during static and dynamic balance. The XCoM method was found to be applicable to dynamic balance as well as static balance.

Keywords: Centre of Mass, static balance, Dynamic balance, extrapolated Centre of Mass

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: C. J. W. Habets, D. J. Peters, J. G. de Gijt, A. V. Metrikine, S. N. Jonkman

Abstract:

Conventional seismic designs of quay walls in ports are mostly based on pseudo-static analysis. A more advanced alternative is the Performance-Based Design (PBD) method, which evaluates permanent deformations and amounts of (repairable) damage under seismic loading. The aim of this study is to investigate the suitability of this method for anchored sheet pile quay walls that were not purposely designed for seismic loads. A research methodology is developed in which pseudo-static, permanent-displacement and finite element analysis are employed, calibrated with an experimental reference case that considers a typical anchored sheet pile wall. A reduction factor that accounts for deformation behaviour is determined for pseudo-static analysis. A model to apply traditional permanent displacement analysis on anchored sheet pile walls is proposed. Dynamic analysis is successfully carried out. From the research it is concluded that PBD evaluation can effectively be used for seismic analysis and design of this type of structure.

Keywords: Anchored sheet pile quay wall, simplified dynamic analysis, performance-based design, pseudo-static analysis.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: D.N. Zheng, J.X. Wang, Y.N. Zhao, Z.H. Yang

Abstract:

The Linear discriminant analysis (LDA) can be generalized into a nonlinear form - kernel LDA (KLDA) expediently by using the kernel functions. But KLDA is often referred to a general eigenvalue problem in singular case. To avoid this complication, this paper proposes an iterative algorithm for the two-class KLDA. The proposed KLDA is used as a nonlinear discriminant classifier, and the experiments show that it has a comparable performance with SVM.

Keywords: Linear discriminant analysis (LDA), kernel LDA (KLDA), conjugate gradient algorithm, nonlinear discriminant classifier.

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Authors: Mohammad Moeini, Mehrdad Ghyabi, Kiarash Mohtasham Dolatshahi

Abstract:

This paper investigates seismic soil-pile interaction using the Beam on Nonlinear Winkler Foundation (BNWF) approach. Three soil types are considered to cover all the possible responses, as well as nonlinear site response analysis using finite element method in OpenSees platform. Excitations at each elevation that are output of the site response analysis are used as the input excitation to the soil pile system implementing multi-support excitation method. Spectral intensities of acceleration show that the extent of the response in sand is more severe than that of clay, in addition, increasing the PGA of ground strong motion will affect the sandy soil more, in comparison with clayey medium, which is an indicator of the sensitivity of soil-pile systems in sandy soil.

Keywords: Beam on nonlinear Winkler foundation method, multi-support excitation, nonlinear site response analysis, seismic soil-pile interaction.

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Authors: Ahmed Mohammed Youssef Mohammed, Mohammad Reza Okhovat, Koichi Maekawa

Abstract:

Small-scale RC models of both piles and tunnel ducts were produced as mockups of reality and loaded under soil confinement conditionsto investigate the damage evolution of structural RC interacting with soil. Experimental verifications usinga 3D nonlinear FE analysis program called COM3D, which was developed at the University of Tokyo, are introduced. This analysis has been used in practice for seismic performance assessment of underground ducts and in-ground LNG storage tanks in consideration of soil-structure interactionunder static and dynamic loading. Varying modes of failure of RCpilessubjected to different magnitudes of soil confinement were successfully reproduced in the proposed small-scale experiments and numerically simulated as well. Analytical simulation was applied to RC tunnel mockups under a wide variety of depth and soil confinement conditions, and reasonable matching was confirmed.

Keywords: Soil-Structure Interaction, RC pile, RC Tunnel

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: Yashar Haghighatfar, Shahrzad Mirhosseini

Abstract:

Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage.

Keywords: MEMS, pull-in instability, electrostatically actuated microbeam, reduced order method.

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Authors: K. Elleuch, A. Chaari

Abstract:

This paper deals with modeling and parameter identification of nonlinear systems described by Hammerstein model having Piecewise nonlinear characteristics such as Dead-zone nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the triangular basis functions leads to a particular form of Hammerstein model. The approximation by using Triangular basis functions for the description of the static nonlinear block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD) technique has been applied to separate the coupled parameters. The proposed approach has been efficiently tested on academic examples of simulation.

Keywords: Identification, Hammerstein model, Piecewisenonlinear characteristic, Dead-zone nonlinearity, Triangular basisfunctions, Singular Values Decomposition

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Authors: Farhad Asadi, Gholamhasan Payganeh

Abstract:

High-speed turbomachine can experience significant centrifugal and gas bending loads. As a result, the compressor blades must be able to resist high-frequency oscillations due to surge or stall condition in flow field dynamics. In this paper, vibration characteristics of the 6th stage blade compressor have been examined in detail with, using 3-D finite element (FE) methods. The primary aim of this article is to gain an understanding of nonlinear vibration induced in the blade against different loading conditions. The results indicate the nonlinear behavior of the blade as a result of the amplitude of resonances or material properties. Since one of the leading causes of turbine blade failure is high cycle fatigue, simulations were started by specifying the stress distribution in the blade due to the centrifugal rotation. Next, resonant frequencies and critical speeds of the blade were defined by modal analysis. Finally, the harmonic analysis was simulated on the blades.

Keywords: Nonlinear vibration, modal analysis, resonance, frequency response, compressor blade.

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Authors: A. Bahmanikashkouli, O.R. Bahadori Nezhad

Abstract:

In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

Keywords: Generalized Differential Quadrature method, Nonlinear consolidation, Nonlinear system of equations, Time-varied drainage

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Authors: T. H. Lee, J. H. Park, S. M. Lee, S. C. Lee

Abstract:

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of load current is the significant one of these for good performance of the SOFC system. In order to keep the constant stack terminal voltage by changing load current, the nonlinear model predictive control (MPC) is proposed in this paper. After primary control method is designed to guarantee the fuel utilization as a proper constant, a nonlinear model predictive control based on the Wiener model is developed to control the stack terminal voltage of the SOFC system. Simulation results verify the possibility of the proposed Wiener model and MPC method to control of SOFC system.

Keywords: SOFC, model predictive control, Wiener model.

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Authors: Sandeep Sharma, Sarabjit Singh, Meenakshi Sharma

Abstract:

Load balancing is the process of improving the performance of a parallel and distributed system through a redistribution of load among the processors [1] [5]. In this paper we present the performance analysis of various load balancing algorithms based on different parameters, considering two typical load balancing approaches static and dynamic. The analysis indicates that static and dynamic both types of algorithm can have advancements as well as weaknesses over each other. Deciding type of algorithm to be implemented will be based on type of parallel applications to solve. The main purpose of this paper is to help in design of new algorithms in future by studying the behavior of various existing algorithms.

Keywords: Load balancing (LB), workload, distributed systems, Static Load balancing, Dynamic Load Balancing

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: Cai-Wan Chang-Jian

Abstract:

This study presents a systematic analysis of the dynamic behaviors of a gear-bearing system with porous squeeze film damper (PSFD) under nonlinear suspension, nonlinear oil-film force and nonlinear gear meshing force effect. It can be found that the system exhibits very rich forms of sub-harmonic and even the chaotic vibrations. The bifurcation diagrams also reveal that greater values of permeability may not only improve non-periodic motions effectively, but also suppress dynamic amplitudes of the system. Therefore, porous effect plays an important role to improve dynamic stability of gear-bearing systems or other mechanical systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Keywords: Gear, PSFD, bifurcation, chaos.

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Authors: Gilberto Gonzalez-A , Israel Nuñez

Abstract:

A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Keywords: Bond graph, nonlinear observer, electrical transformer, nonlinear saturation.

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Authors: Migbar Assefa

Abstract:

The performance of a machine tool is eventually assessed by its ability to produce a component of the required geometry in minimum time and at small operating cost. It is customary to base the structural design of any machine tool primarily upon the requirements of static rigidity and minimum natural frequency of vibration. The operating properties of machines like cutting speed, feed and depth of cut as well as the size of the work piece also have to be kept in mind by a machine tool structural designer. This paper presents a novel approach to the design of machine tool column for static and dynamic rigidity requirement. Model evaluation is done effectively through use of General Finite Element Analysis software ANSYS. Studies on machine tool column are used to illustrate finite element based concept evaluation technique. This paper also presents results obtained from the computations of thin walled box type columns that are subjected to torsional and bending loads in case of static analysis and also results from modal analysis. The columns analyzed are square and rectangle based tapered open column, column with cover plate, horizontal partitions and with apertures. For the analysis purpose a total of 70 columns were analyzed for bending, torsional and modal analysis. In this study it is observed that the orientation and aspect ratio of apertures have no significant effect on the static and dynamic rigidity of the machine tool structure.

Keywords: Finite Element Modeling, Modal Analysis, Machine tool structure, Static Analysis.

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Authors: K. Abuzayan, H. Alabed, K. Zarug

Abstract:

The objectives of this study (baseline study, n = 20) were to implement Matlab procedures for quantifying selected static  balance variables, establish baseline data of selected variables which characterize static balance activities in a population of healthy young adult males, and to examine any trial effects on these variables. The results indicated that the implementation of Matlab procedures for quantifying selected static balance variables was practical and enabled baseline data to be established for selected variables. There was no significant trial effect. Recommendations were made for suitable tests to be used in later studies. Specifically it was found that one foot-tiptoes tests either in static balance is too challenging for most participants in normal circumstances. A one foot-flat eyes open test was considered to be representative and challenging for static balance.

Keywords: Static Balance, Base of support, Baseline Data.

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Authors: S. H. Teh, S. Malawaraarachci, W. P. Chan, A. Nassirharand

Abstract:

The purpose of this paper is to present the design and instrumentation of a new benchmark multivariable nonlinear control laboratory. The mathematical model of this system may be used to test the applicability and performance of various nonlinear control procedures. The system is a two degree-of-freedom robotic arm with soft and hard (discontinuous) nonlinear terms. Two novel mechanisms are designed to allow the implementation of adjustable Coulomb friction and backlash.

Keywords: Nonlinear control, describing functions, AdjustableCoulomb friction, Adjustable backlash.

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Authors: S. H. Yahaya, J. M. Ali, M. R. Arham

Abstract:

This paper presents the analysis of duct design using static and dynamic approaches. The static approach is used to find out applicability between the design and material applied. The material used in this paper is Thermoplastic Olefins (TPO). For the dynamic approach, the focusing is only on the CFD simulations. The fatigue life in this design and material applied also covered.

Keywords: CFD, structural analysis, fluid analysis, duct design, fatigue life

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Authors: B.P. Bezruchko, D.A. Smirnov

Abstract:

Quantitative characterization of nonlinear directional couplings between stochastic oscillators from data is considered. We suggest coupling characteristics readily interpreted from a physical viewpoint and their estimators. An expression for a statistical significance level is derived analytically that allows reliable coupling detection from a relatively short time series. Performance of the technique is demonstrated in numerical experiments.

Keywords: Nonlinear time series analysis, directional couplings, coupled oscillators.

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Authors: Meftah Ali

Abstract:

This article aims to analyze the static stability and pseudostatic slope by using different methods such as: Bishop method, Junbu, Ordinary, Morgenstern-price and GLE. The two dimensional modeling of slope stability under various loading as: the earthquake effect, the water level and road mobile charges. The results show that the slope is stable in the static case without water, but in other cases, the slope lost its stability and give unstable. The calculation of safety factor is to evaluate the stability of the slope using the limit equilibrium method despite the difference between the results obtained by these methods that do not rely on the same assumptions. In the end, the results of this study illuminate well the influence of the action of water, moving loads and the earthquake on the stability of the slope.

Keywords: Slope stability, pseudo static, safety factor, limit equilibrium.

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Authors: M. Seguini, D. Nedjar

Abstract:

An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: Finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability.

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Authors: Blaise Fyama, Elie Museng, Grace Mukoma

Abstract:

In this article we present a java implementation of video telephony using the SIP protocol (Session Initiation Protocol). After a functional analysis of the SIP protocol, we relied on the work of Italian researchers of University of Parma-Italy to acquire adequate libraries for the development of our own communication tool. In order to optimize the code and improve the prototype, we used, in an incremental approach, test techniques based on a static analysis based on the evaluation of the complexity of the software with the application of metrics and the number cyclomatic of Mccabe. The objective is to promote the emergence of local start-ups producing IP video in a well understood local context. We have arrived at the creation of a video telephony tool whose code is optimized.

Keywords: Static analysis, coding, complexity, mccabe metrics, Sip, uml.

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Authors: A. Pashkevich, A. Klimchik, D. Chablat

Abstract:

The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide family

Keywords: Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator

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