Showing papers in "International Journal of Structural Stability and Dynamics in 2008"
TL;DR: In this article, a dynamic finite element model of a railway concrete sleeper in a track system is presented, aimed at raising the consideration of dynamic effects in sleeper design, and the numerical analyses present the ratio between the dynamic and the static bending moment resultants, the dynamic magnification factor, of the railway concrete sleepers under different sinusoidal pulse durations.
Abstract: Railway sleepers in a track system are usually subjected to a wide range of loading conditions. A critical type of loading condition that causes cracking in the railway concrete sleepers is the dynamic transient wheel force. The transient wheel forces are often due to wheel or rail abnormalities. This paper presents a dynamic finite element model of a railway concrete sleeper in a track system, aimed at raising the consideration of dynamic effects in sleeper design. The railway concrete sleeper is modeled using the beam-on-elastic-foundation theory. Since in the actual tracks the ballast underneath does not provide any tensile resistance, the finite beam elements employed in this investigation take into account the bending and shear deformations, together with the tensionless nature of the elastic support. This paper places emphasis on the effect of the transient periods on the flexural responses of railway sleepers in track systems. Using the robust finite element software STRAND7, the finite element model of the railway concrete sleeper was previously established and validated against experimental data by the authors. The numerical analyses present the ratio between the dynamic and the static bending moment resultants, the dynamic magnification factor, of the railway concrete sleeper under different sinusoidal pulse durations.
45 citations
TL;DR: In this paper, the orthogonality condition between the natural modes is utilized to decouple the equations of motion for partial composite beams with partial shear connections, and the fundamental frequency and deflection impact factor of simple composite beams are identified.
Abstract: This paper is concerned with the dynamic characteristics of composite beams with partial shear connections. The governing equations of motion for partial composite beams are derived from the one-dimensional partial composite beam theory. By solving the corresponding characteristic equation, the natural frequencies and modal shapes for simple partial composite beams are obtained. The orthogonality condition between the natural modes is utilized to decouple the equations of motion. Closed-form solution for the simple partial composite beam subjected to a moving load is derived by the modal superposition method. Key parameters that govern the fundamental frequency and deflection impact factor of simple partial composite beams are identified. Numerical results show that the former is controlled by the composite connection and section combination parameters, and the latter by the fundamental frequency ratio. It was observed that the time-history response of a partial composite beam may differ significantly from that of a full composite beam in terms of amplitude, period, and overall shape, depending on the composition connection.
31 citations
TL;DR: In this article, the authors investigated the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia.
Abstract: In this paper, we investigate the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but the Poisson ratios of the FGM plates and shells are assumed to be constant. The expressions for the membrane, bending and shear stiffness of FGM shell elements are more a complicated combination of material properties than a homogeneous element. In order to validate the finite element numerical solutions, the Navier solutions for rectangular plates based on the first order shear deformation theory are also presented. The present numerical solutions for composite and sigmoid FGM (S-FGM) plates and shells are verified by the Navier solutions and various examples of composite and FGM structures. The present results are in good agreement with the Navier theoretical solutions.
31 citations
TL;DR: In this article, a geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out, where the Green-Lagrange strain tensor in its entirety is used in the analysis.
Abstract: Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form.
30 citations
TL;DR: In this paper, a statistical model updating technique for damage detection of underwater pipeline systems via vibration measurements was presented, which includes a plastic pipe and some removable springs which are designed and fabricated to link the pipe and the steel base to simulate the bedding conditions.
Abstract: This paper presents a statistical model updating technique for damage detection of underwater pipeline systems via vibration measurements. To verify the reliability of the method, laboratory tests of a scaled pipeline model were carried out in a towing tank. The model includes a plastic pipe and some removable springs which are designed and fabricated to link the pipe and the steel base to simulate the bedding conditions. Different damage scenarios, in terms of location and severity of scouring under the pipe, were simulated by removing one or several springs. The natural frequencies, damping ratios and mode shapes of the pipeline system were extracted from the measured vibrations using a stochastic subspace identification technique. Both the numerical and the experimental results show that the method is effective and reliable in identifying the underwater pipeline bedding conditions and the damage in the pipe structure.
24 citations
TL;DR: In this paper, a beam element is derived for the thermal-dynamic coupling analysis by the updated Lagrangian formulation and the nodal transformation matrix of the element is obtained by dividing the rigid body rotation of the beam element into the relative translational displacements and axial rotation.
Abstract: In this paper, a beam element is derived for the thermal–dynamic coupling analysis by the updated Lagrangian formulation. The nodal transformation matrix of the element is obtained by dividing the rigid body rotation of the beam element into the relative translational displacements and axial rotation. With this transformation matrix, the interaction between the structural deformation and the absorbed heat flux can be formulated and the thermal–structural coupling effect is thus considered. The validity of the proposed method is illustrated by comparing the obtained results with the numerical, analytical or experimental results available in the literature. Then the method is employed to analyze the thermal–structural responses of the Hubble Space Telescope (HST) solar array. From the results, a reasonable explanation can be given for the failure of the telescope in 1990.
23 citations
TL;DR: In this paper, the application of semiactive devices for controlling the earthquake response of two highway bridges of different cross sections and pier heights is described, which consists of a three-span continuous deck supported on the piers and abutments.
Abstract: This paper describes the application of semiactive devices for controlling the earthquake response of two highway bridges of different cross sections and pier heights Each of the bridges consists of a three-span continuous deck supported on the piers and abutments Semiactive devices such as the magnetorheological damper, the variable friction damper and the variable stiffness device are considered as the control devices These devices are inserted between the deck and piers or abutments of the isolated bridge The semiactive device changes its properties according to the structural response and adds control forces to the system Each pier supporting the bridge is modeled as a linear lumped mass system The optimum parametric values of the semiactive dampers are evaluated and considered in analysis of the bridge A comparative study is performed for different semi-active devices installed on the bridges under different seismic loadings in the longitudinal direction The behaviors of the bridges with different semiactive isolation devices are compared with the corresponding nonisolated ones The semiactive dampers are observed as an effective protective device in reducing the displacements of the isolation bridges as well as the base shear of the piers
22 citations
TL;DR: In this article, the authors considered the vibration and stability problems of a slender column subjected to generalized load with a force directed toward the positive pole, where the load is developed by heads composed of circular profile elements.
Abstract: Considered herein is the vibration and stability problems of a slender column subjected to generalized load with a force directed toward the positive pole. The load is developed by heads composed of circular profile elements. The geometrically nonlinear problem of stability and free vibrations is formulated on the basis of Hamilton's principle, and due to nonlinearity, the problem is solved by applying the small parameter method. Vibration and stability results show the influence of chosen parameters that characterize the considered column (including initial prestressing). The assumed mathematical model is validated by experimental results.
21 citations
TL;DR: In this article, a semi-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends is used for nonlinear dynamic analysis of frames with material and geometric nonlinearities.
Abstract: This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.
18 citations
TL;DR: In this paper, a postbuckling analysis for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression is presented.
Abstract: A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Karman–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.
17 citations
TL;DR: In this article, the peak story drifts of a building structure during earthquakes are used as an indicator of structural demands, and an approximate approach to construct the seismic fragility curves for various states of damage for frame structures is developed.
Abstract: A seismic fragility analysis of structures is essential to prediction of the building behavior that is likely to occur during earthquakes. Normally, the probability of failure of a structure over a specified period of time is obtained through a convolution of the fragility curve with the seismic hazard curve for the structure site. The fragility models and damage states probabilities serve as a basis for improving the structural codes and performance-based design. Thus, there is a need for relatively simple procedures for evaluating fragility data for decision-making. In this study, the peak story drifts of a building structure during earthquakes are used as an indicator of structural demands. An analytical solution for evaluating the statistical characteristics of peak story drifts of frame structures during earthquakes is proposed. Based on it, an approximate approach to constructing the seismic fragility curves for various states of damage for frame structures is developed.
TL;DR: In this article, the authors presented a highly accurate method for analyzing the critical shear buckling load of thin elastic rectangular plates by using the quintic table in place of the complex quintic B-spline functions.
Abstract: This paper presents a highly accurate method for analyzing the critical shear buckling load of thin elastic rectangular plates. The solutions are approximated by the extended spline collocation method (SCM). Using the quintic table in place of the complex quintic B-spline functions, one can easily formulate the field equation of shear buckling loads for a thin elastic rectangular plate. Through the generalized eigenvalue analysis, the shear buckling loads and mode shapes for the plate can be determined precisely. Numerical examples are given for the critical shear buckling load of plates with various combinations of boundary conditions, aspect ratios, and uni- and bi-directional compressive/tensile loadings. The solutions obtained by the SCM are compared with those by the finite element method, the Lagrangian multiplier method, and the extended Kantorovich method under several types of boundary conditions. Compared with the other methods, the proposed SCM is not only more accurate, but also easier for computation.
TL;DR: In this article, the authors investigated the applicability of the wavelet transform to damage detection of a beam-spring structure by burning out the string that is connected to the cantilever beam, and there results an abrupt change or impulse in the discrete wavelet-transformed signal.
Abstract: Presented herein is an experiment that aims to investigate the applicability of the wavelet transform to damage detection of a beam–spring structure. By burning out the string that is connected to the cantilever beam, high-frequency oscillations are excited in the beam–spring system, and there results an abrupt change or impulse in the discrete-wavelet-transformed signal. In this way, the discrete wavelet transform can be used to recognize the damage at the moment it occurs. In the second stage of damage detection, the shift of frequencies and damping ratios is identified by the continuous wavelet transform so as to ensure that the abrupt change or impulse in the signal from the discrete wavelet transform is a result of the damage and not the noise. For the random forced vibration, the random decrement technique is used on the original signal to obtain the free decaying responses, and then the continuous wavelet transform is applied to identify the system parameters. Some developed p version elements are used for the parametric studies on the first stage of health monitoring and to find the damage location. The results show that the two-stage method is successful in damage detection. Since the method is simple and computationally efficient, it is a good candidate for on-line health monitoring and damage detection of structures.
TL;DR: In this article, the large-amplitude free vibration problem of uniform slender pipes conveying fluid on a Pasternak foundation is studied using the principle of conservation of total energy.
Abstract: The large-amplitude free vibration problem of uniform slender pipes conveying fluid on a Pasternak foundation is studied using the principle of conservation of total energy. The temporal equation governing the large-amplitude vibrations is directly obtained from this approach by assuming a suitable admissible spatial function that satisfies the boundary conditions of the pipes. It is solved by using a standard numerical integration scheme. The numerical results, in the form of the ratio of the fundamental nonlinear frequency to the linear frequency for both the simply supported and clamped pipes conveying fluid, are presented in tables and figures for various amplitude parameters, flowing velocities of the internal fluid, and the two stiffness parameters of the Pasternak foundation.
TL;DR: In this article, the effects of randomness in the material properties and foundation stiffness parameters on the elastic buckling of laminated composite plate resting on elastic foundation subjected to uniform in-plane edge compression are studied.
Abstract: In this paper, the effects of randomness in the material properties and foundation stiffness parameters on the elastic buckling of laminated composite plate resting on elastic foundation subjected to uniform in-plane edge compression are studied. Higher order shear deformation theory has been used for the plates. The interaction between the plate and foundation is included in the formulation of a two-parameter Pasternak model. A C0 finite element method is used for treating the random eigenvalue problem. The uncertain lamina material properties and the foundation stiffness parameters are modeled as independent basic random variables. A mean-centered first order perturbation technique is adopted to examine the stochastic characteristics of the buckling load. From the results presented for laminated composite plates resting on elastic foundations with different boundary conditions, the influence of variation of material constant, foundation stiffness parameters, edge in-plane forces, side-to-thickness ratio, plate aspect ratio, and variation in standard deviation of material properties on the buckling response has been investigated. The results have been compared with those available in the literature and from an independent Monte Carlo simulation.
TL;DR: In this article, a 20-story building is considered as a shear frame and reduced to an SDOF system by means of the mode-superposition method, and the system is subjected to harmonic load and numerical searches are conducted based on the Min Max procedure in order to obtain efficient interconnected (I) multiple tuned mass dampers.
Abstract: In this paper, the dynamic performance of a controlled high building is numerically investigated considering the effects of different numbers of mass dampers and their interconnection The numerical analysis is conducted on a 20-story building considered as a shear frame and reduced to an SDOF system by means of the mode-superposition method The system is subjected to harmonic load Numerical searches are conducted based on the Min Max procedure in order to obtain efficient interconnected (I) multiple tuned mass dampers (MTMD) Comparisons are made among the uncontrolled system, the system controlled by non-interconnected (NI) MTMD, and the system controlled by (I) MTMD in frequency and time domain Both (NI) and (I) MTMD reduce significantly frequency response peak amplitude It is observed that the (I) MTMD produces great reductions on maximum displacement, rms displacement, steady-state peak response, and story displacements close to the reductions obtained by (NI) MTMD using review parameters Mass maximum displacements analysis shows that the space required for (I) MTMD installation is smaller than (NI) MTMD
TL;DR: Simulation results show that, by using the frequencies of the structures under control, the proposed damage indicators are more sensitive to damage and are capable of detecting and locating small damage of structures.
Abstract: A statistical method using frequencies of structures under control is proposed for detecting damage. In the study, feedback control based on independent modal space control is first used to assign the pole of the system under detection intentionally. Then the prescribed characteristic frequencies of the structure under control, which may be more sensitive to damage, are obtained and further employed to constitute a sensitivity-enhanced damage indicator (SEDI). The principle of sensitivity-enhancing feedback control for damage detection of multi-degree-of-freedom systems is elaborated. To overcome the effect of measurement noise on modal frequencies, a hypothesis test involving the t-test that utilizes the SEDI is employed to estimate the occurrence of damage, while a statistical pattern recognition method that uses the feature vectors including the SEDI is employed to locate damage. Based on the perturbation theory, the feature vectors are normalized in order to eliminate the effect of damage extent on damage localization. The proposed method is verified by examples including a three-span continuous beam with a single damaged element and the IASC-ASCE benchmark structure with a single damaged brace. Simulation results show that, by using the frequencies of the structures under control, the proposed damage indicators are more sensitive to damage and are capable of detecting and locating small damage of structures.
TL;DR: In this article, the stability of the pylons of a cable-stayed bridge under the action of time-dependent loads, due to the vibration of the bridge deck, is investigated.
Abstract: This paper deals with the stability of the pylons of a cable-stayed bridge under the action of time-dependent loads, due to the vibration of the bridge deck. The stability of such problems of cable-stayed bridges is solved by a technique developed in the Laboratory of Metal Structures and Steel Bridges, of National Technical University of Athens (NTUA), as well as Bolotin's technique for the solution of nonlinear problems of dynamic stability. Three cases are studied: pylons with damping, pylons under forced vibration, and pylons subjected to an arbitrary external dynamic load. Useful relations are established by the aforementioned solution method, examples for a variety of pylons are presented, and interesting results regarding the stability of each case are given in diagrams.
TL;DR: In this paper, the effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method, and the results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel.
Abstract: The present study deals with the dynamic stability of laminated composite pre-twisted cantilever panels. The effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method. The first-order shear deformation theory is used to model the twisted curved panels, considering the effects of transverse shear deformation and rotary inertia. The results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel. The instability occurs later for square than rectangular twisted panels. The onset of instability occurs later for pre-twisted cylindrical panels than the flat panels due to addition of curvature. However, the spherical pre-twisted panels show small increase of nondimensional excitation frequency.
TL;DR: In this paper, the vibration and damping of a hollow sandwich box column containing a viscoelastic layer (VEL) or an electrorheological (ER) or magnetorheological fluid core with a constraining layer are analyzed and a comparison of performance is made.
Abstract: In this paper, the vibration and damping of a hollow sandwich box column containing a viscoelastic layer (VEL) or an electrorheological (ER) or magnetorheological (MR) fluid core with a constraining layer are analyzed and a comparison of performance is made. The hollow sandwich box column comprises two skin plates and a VEL/ER/MR fluid core layer. The finite element method is used to study the vibration and damping behaviors of the column. The natural frequencies and modal loss factors are obtained by solving the complex eigenvalue problem. The modal dampings and natural frequencies of the column are calculated for various electric as well as magnetic fields and their performance is compared with that of the viscoelastic core layer for the clamped-free boundary condition. Effects of core thickness, electric voltage and magnetic field on the vibration behavior of the sandwich box column are investigated.
TL;DR: In this paper, an elastic beam theory is developed to predict the buckling strain of defective CNTs, and the strain prediction via the continuum mechanics model is verified from comparison studies by molecular dynamics simulations.
Abstract: This technical note is concerned with the buckling of single-walled carbon nanotubes with one atomic vacancy. An elastic beam theory is developed to predict the buckling strain of defective CNTs, and the strain prediction via the continuum mechanics model is verified from comparison studies by molecular dynamics simulations. The results demonstrate the effectiveness of the continuum mechanics theory for longer CNTs. In addition, a local kink is revealed in the morphology of the buckling of shorter defective CNTs via molecular dynamics.
TL;DR: In this paper, free vibration analysis of Timoshenko piles partially embedded in elastic soil, semi-rigidly connected at the upper end, and subjected to an axial force is concerned.
Abstract: This paper is concerned with the free vibration analysis of Timoshenko piles partially embedded in elastic soil, semi-rigidly connected at the upper end, and subjected to an axial force. The pile is divided into three regions: the pile portion above the soil constitutes the first region, while the second and third regions are the pile portion that is embedded in two different layers of the soil type. The pile material is assumed to be linearly elastic and the axial force is constant along the pile length. The soil is idealized by the Winkler model and the semi-rigid connection of the pile is modeled by a rotational spring. The natural frequencies of the piles are calculated from the transfer matrix for different axial forces, rotational spring constants, subgrade reaction moduli and embedded lengths of the pile. The results indicate that the natural frequency of the pile decreases as the axial force increases. Further, the increase in the stiffness of the rotational spring at the upper end of the pile causes only a small increase in the natural frequency. Finally, both the pile length and the subgrade reaction of the soil influence significantly the natural frequency of the pile.
TL;DR: In this paper, the dynamic stability of a rotating disk rotating in air has been modeled and analyzed numerically as well as observed from experiments, and a simple expression on the aerodynamic loading acting on the rotating disk is applied in the modeling, and dynamic stability results of the disks are evaluated based on the eigenvalues for the vibration modes.
Abstract: In this paper, the dynamic stability of a disk rotating in air has been modeled and analyzed numerically as well as observed from experiments. A simple expression on the aerodynamic loading acting on the rotating disk is applied in the modeling, and the dynamic stability results of the disks are evaluated based on the eigenvalues for the vibration modes. The disk critical speeds and the flutter speeds are calculated and compared with the results from experiments, which are conducted on two steel disks with different diameters and thicknesses. The modeling predicts that the rotating disk flutter starts with the mode (0, 3)B, which agrees with the results reported in the literature and the observation in the present experimental study.
TL;DR: In this paper, the principal resonance of a cantilever with a contact end was investigated using the Derjaguin-Muller-Toporov theory and the Lyapunov-linearized stability theory.
Abstract: In this paper, the principal resonance is investigated for a cantilever with a contact end. The cantilever is modeled as an Euler–Bernoulli beam, and the contact is modeled by the Derjaguin–Muller–Toporov theory. The problem is formulated as a linear nonautonomous partial-differential equation with a nonlinear autonomous boundary condition. The method of multiple scales is applied to determine the steady-state response. The equation of response curves is derived from the solvability condition of eliminating secular terms. The stability of steady-state responses is analyzed by using the Lyapunov-linearized stability theory. Numerical examples are presented to highlight the effects of the excitation amplitude, the damping coefficient, and the coefficients related to the contact.
TL;DR: In this paper, the prebuckling dynamics of transversely isotropic thin cylinder shells in the context of propagation and reflection of axial stress waves were investigated and the Hamiltonian system of the governing equation was obtained directly and rationally without the need for any trial shape functions, such as the classical semi-inverse method.
Abstract: This paper investigates the prebuckling dynamics of transversely isotropic thin cylinder shells in the context of propagation and reflection of axial stress waves. By constructing the Hamiltonian system of the governing equation, the symplectic eigenvalues and eigenfunctions are obtained directly and rationally without the need for any trial shape functions, such as the classical semi-inverse method. The critical loads and buckling models are reduced to the problem of eigenvalues and eigensolutions, in which zero-eigenvalue solutions and nonzero-eigenvalue solutions correspond to axisymmetric buckling and nonaxisymmetric buckling, respectively. Numerical results reveal that energy is concentrated at the unconstrained free ends of the shell and the buckling modes have bigger bell-mouthed shapes at these positions.
TL;DR: In this paper, a new third order approximate function is presented for the structural response quantities, as functions of the cross-sectional properties, and four different methods for the optimum design are defined based on this approximate function.
Abstract: Presented herein are four different methods for the optimum design of structures subject to multiple natural frequency constraints. During the optimization process the optimum cross-sectional dimensions of elements are determined. These methods are robust and efficient in terms of the number of eigenvalue analyses required, as well as the overall computational time for the optimum design. A new third order approximate function is presented for the structural response quantities, as functions of the cross-sectional properties, and four different methods for the optimum design are defined based on this approximate function. The main features of the proposed function are that only the diagonal terms of higher order derivative matrices are employed, and these derivatives are established by the available first order derivatives. The first order exact derivatives are obtained from a sensitivity analysis at the previous design points. We show that this approximate function creates high quality approximations of the structural responses, such as the frequencies. Examples are presented and the efficiency and quality of the proposed methods are discussed and compared.
TL;DR: In this article, a change in the representation of discrete motion equations for nonlinear structural dynamics of two-dimensional bodies is developed, which leads to a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations.
Abstract: A change in the representation of discrete motion equations for nonlinear structural dynamics of two-dimensional bodies is developed. The objective is to write the motion equation in a less nonlinear form. This leads to a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration step.
TL;DR: In this article, the numerical properties of a subfamily of the HHT-α integration method with -⅓ ≤ α ≤ 0, β = ¼(1 - α)2 and γ = ½-α for the solution of nonlinear systems are analytically explored using a linearized analysis, where the stiffness term in total form is used to determine the restoring force.
Abstract: The HHT-α method previously developed shows favorable numerical dissipation, in addition to unconditional stability, in the solution of linear elastic systems. However, its performance in the solution of nonlinear systems has not been studied yet. In this paper, the numerical properties of a subfamily of this integration method with -⅓ ≤ α ≤ 0, β = ¼(1 - α)2 and γ = ½-α for the solution of nonlinear systems are analytically explored using a linearized analysis, where the stiffness term in total form is used to determine the restoring force. A theoretical proof of unconditional stability for nonlinear systems is presented. The subfamily of the integration method is verified to possess favorable numerical dissipation for both linear and nonlinear systems. Period distortion affected by the step degree of either nonlinearity or convergence is studied. Although the analysis is conducted for a single-degree-of-freedom nonlinear system, the application to a multiple-degree-of-freedom nonlinear system is also illustrated. It is confirmed that the performance of the HHT-α method for nonlinear systems is generally the same as that for linear elastic systems, except for the high dependence on the step degree of nonlinearity.
TL;DR: In this article, the basic set of equations for nonlinear electromagnetic elasticity vibration expressed by the displacement of a thin plate in a longitudinal and a transverse magnetic field is obtained, respectively.
Abstract: Based on the Maxwell equations, the electromagnetic constitutive relations and boundary condition, the electrodynamic equation and the electromagnetic force expressions in an electromagnetic field are derived. Using the principle of virtual work, the basic set of equations for nonlinear electromagnetic elasticity vibration expressed by the displacement of a thin plate in a longitudinal and a transverse magnetic field is obtained, respectively. In addition, we study the nonlinear principal resonance and the solution stability of a thin plate with two opposite sides simply supported and subjected to a mechanical live load and in a constant transverse magnetic field. By the method of multiple scales, the amplitude frequency response equation and the approximate analytic solution in steady motion are also derived. According to the characteristic of singularity and the Lyapunov stability theory, the stability of the solution is analyzed and the critical condition of stability is determined. Finally, by means of numerical calculations, the amplitude frequency response curves, time history response plots and phase charts of the magnetoelasticity vibration are obtained.
TL;DR: In this article, a 3D moving least square Ritz (MLS-Ritz) formulation for free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints is presented.
Abstract: This paper presents a three-dimensional (3D) moving least-square Ritz (MLS-Ritz) formulation for the free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints. The analysis is based on the linear elasticity theory. The Ritz trial functions are established through the moving least-square technique for the displacement fields of the plates. Vibration frequencies for thick square plates and right-angled isosceles triangular plates are obtained by the MLS-Ritz method. The reliability and accuracy of the presented method are examined by extensive convergence and comparison studies and it is established herein that the MLS-Ritz method is a powerful and effective numerical method for the 3D analysis of thick plates.