The Experts below are selected from a list of 7308 Experts worldwide ranked by ideXlab platform
M Shariyat - One of the best experts on this subject based on the ideXlab platform.
-
nonlinear thermomechanical Dynamic Buckling analysis of imperfect viscoelastic composite sandwich shells by a double superposition global local theory and various constitutive models
Composite Structures, 2011Co-Authors: M ShariyatAbstract:Abstract Almost no Dynamic Buckling analysis has been performed so far for the sandwich/multilayer viscoelastic shells. Even the vibration analyses of the mentioned shells have been restricted to the harmonic loads ignoring the transverse stresses and their continuity at the mutual interfaces of the layers, and the transverse flexibility of the shell. In the present paper, a high-order double-superposition global–local theory inherently suitable for nonlinear analyses is proposed and employed for nonlinear Dynamic Buckling and postBuckling analyses of imperfect viscoelastic composite/sandwich cylindrical shells subjected to thermomechanical loads. Depending on the nature of the applied loads, both complex modulus and hierarchical constitutive models are used for the viscoelastic materials. Results reveal that as the time duration of the suddenly applied loads decreases beyond the first natural period of the shell, the Dynamic Buckling load becomes much higher than the static Buckling load, especially for the rectangular load–time histories. Furthermore, the relaxation behavior of the viscoelastic material may decrease the Dynamic Buckling load.
-
a double superposition global local theory for vibration and Dynamic Buckling analyses of viscoelastic composite sandwich plates a complex modulus approach
Archive of Applied Mechanics, 2011Co-Authors: M ShariyatAbstract:A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and Dynamic Buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some Dynamic Buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.
-
a nonlinear double superposition global local theory for Dynamic Buckling of imperfect viscoelastic composite sandwich plates a hierarchical constitutive model
Composite Structures, 2011Co-Authors: M ShariyatAbstract:Abstract Nonlinear Dynamic thermo-mechanical Buckling and postBuckling analyses of imperfect viscoelastic composite laminated/sandwich plates are performed by a proposed theory that takes into account all the interlaminar kinematic and transverse stress continuity conditions, for the first time. Even the Dynamic Buckling analysis of the multi-layered/sandwich plates employing the hierarchical constitutive model has not been performed before. The proposed theory is a double-superposition high-order global–local theory that is calibrated based on the nonlinear strain–displacement expressions for the thermoelastic loadings taking into account the structural damping. The Buckling loads are determined based on a criterion previously published by the author. Various complex sensitivity analyses evaluating effects of the relaxation parameters, rate of the loading, sudden heating, and pre-stress on thermo-mechanical Buckling of the viscoelatic multi-layered/sandwich plates are performed. Results show that the viscoelastic behavior may decrease the Buckling load. Sudden Dynamic Buckling loads are higher due to the reflected stress waves.
-
non linear Dynamic thermo mechanical Buckling analysis of the imperfect sandwich plates based on a generalized three dimensional high order global local plate theory
Composite Structures, 2010Co-Authors: M ShariyatAbstract:Abstract The available plate theories either have not considered the interlaminar stress continuity condition or have been calibrated based on linear strain–displacement relations. Moreover, almost all Buckling analyses performed so far employing the global–local plate theories, were restricted to linear, static Buckling analyses of the perfect plates, neglecting the transverse normal strain and stress. Researches available in literature for Dynamic Buckling analyses of the sandwich plates are very rare. In the present paper, a generalized high-order global–local theory that satisfies all the kinematic and transverse stress continuity conditions at the interfaces of the layers, is proposed to investigate Dynamic Buckling of imperfect sandwich plates subjected to thermo-mechanical loads. In comparison to the layerwise, mixed, and available global–local theories, the present theory has the advantages of: (1) less required computational time due to using the global–local technique and matrix formulations, (2) higher accuracy due to satisfying the complete interlaminar kinematic and transverse stress continuity conditions and considering the transverse flexibility, (3) suitability for non-linear analyses, (4) capability of investigating the local phenomena, such as the wrinkling. To enhance the accuracy of the results, compatible Hermitian quadrilateral elements are employed. The Buckling loads are determined based on a criterion previously published by the author.
-
Dynamic Buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo electro mechanical loadings considering the temperature dependency of the material properties
Composite Structures, 2009Co-Authors: M ShariyatAbstract:Dynamic Buckling of piezolaminated plates under thermo-electro-mechanical loads has not been investigated so far. In the present paper, effects of the thermo-piezoelasticity on the Dynamic Buckling under suddenly applied thermal and mechanical loads are investigated for imperfect rectangular composite plates with surface-bonded or embedded piezoelectric sensors and actuators. A finite element formulation based on a higher-order shear deformation theory is developed. Both the initial geometric imperfections of the plate and the temperature-dependency of the material properties are taken into account. Complex Dynamic loading combinations include in-plane mechanical loads, heating, and electrical actuations are considered. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly nonlinear governing equations, and an instability criterion already proposed by the author are employed. A simple negative proportional feedback control is used to actively control the transient response of the plate. Results show that Buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. It is also noticed that in many cases, effects of the control voltage on the results may be ignored compared to the temperature-dependency of the material properties and initial geometric imperfections effects.
Haim Abramovich - One of the best experts on this subject based on the ideXlab platform.
-
parametric studies on the Dynamic Buckling phenomenon of a composite cylindrical shell under impulsive axial compression
Journal of Sound and Vibration, 2020Co-Authors: Monika Zaczynska, Haim Abramovich, Chiara BisagniAbstract:Abstract The Dynamic instability of a thin-walled carbon-fibre reinforced composite cylindrical shell is studied. The analysis is performed with the Finite Element code, ABAQUS, estimating the Dynamic Buckling load using the Budiansky–Roth criterion. The influence of the following factors on the Dynamic behaviour of the shell is analysed: the shape of pulse loading, the initial geometric imperfection and the pulse duration. It is found that for short load duration, the structure resistance to pulse loading in the form of Dynamic Buckling load is significantly higher compared to the static Buckling load. As load duration increases, the magnitude of the Dynamic Load Factor (DLF), defined as the ratio between the Dynamic and static Buckling loads, decreases significantly, reaching a value of DLF
-
Dynamic Buckling of a laminated composite stringer stiffened cylindrical panel
Composites Part B-engineering, 2012Co-Authors: H Less, Haim AbramovichAbstract:Abstract The present study deals with the “Dynamic Buckling” of a laminated composite stringer–stiffened curved panel. The “Dynamic Buckling”, in the present study, is concerned with the unbounded lateral response of the panel, which is subjected to an axial impact load. In reinforced panels with widely spaced adequately stiff stringers, the structure may pass through two major states before its total collapse: Buckling of the panel skin between stiffeners and Buckling of the stiffeners themselves. This study focuses on the lowest Buckling load of the stringer–stiffened panel, which is, Buckling of the panel skin between stiffeners. The analysis of the laminated composite stringer–stiffened cylindrical panel was performed by using the commercial ANSYS finite element software. The model simulates the structure and its associated boundary conditions. The boundary conditions simulate the stringer–stiffened cylindrical panel as a part of a fuselage. The static Buckling analysis was performed using the eigenvalue Buckling approach to determine the static critical load. Modal analysis was used to calculate the first natural frequency and corresponding mode shape of the structure. Nonlinear transient Dynamic analysis was used to determine the Dynamic critical load. In the transient Dynamic analysis the Newmark method with the Newton–Raphson scheme were used. In the present study, the equation of motion approach was applied. By this approach, the equations of motion were numerically solved for various load parameter values (loading amplitude and loading duration) to obtain the system response. Special attention was given to the neighborhood of loading durations corresponding to the period of the lowest bending frequency of the skin. For each load duration, the Dynamic Buckling load was calculated using a load versus lateral displacement curve generated by the ANSYS code. The results were plotted on a Dynamic load amplification factor (DLF) graph. The DLF is defined, as the ratio of the Dynamic Buckling to the static Buckling of the panel. For loading periods in the neighborhood of the lowest natural frequency of the panel, the DLF was less than unity. It means that, for those particular loading periods, the Dynamic Buckling load is lower than the static one.
-
Dynamic Buckling of cylindrical stringer stiffened shells
Computers & Structures, 2003Co-Authors: Ronith Yaffe, Haim AbramovichAbstract:Abstract The Dynamic Buckling of cylindrical stringer stiffened shells was investigated both numerically and experimentally. A new criterion to define the numerical “Dynamic” Buckling load was developed yielding consistent results. The ADINA finite element code was applied to simulate the static and Dynamic Buckling loads of the shells. It was shown numerically that when the period of the applied loading (half-wave sine) equals half the lowest natural period of the shell, there is a slight drop in the Dynamic load amplification factor (DLF). The DLF is defined, as the ratio of the Dynamic Buckling to the static Buckling of the shell. This factor drops below unity, when the ratio of the given sound speed in solids, c , to the velocity developed axially due to the applied Dynamic loading, approaches unity. It means that, for this particular loading period, the Dynamic Buckling load would be lower than the static one. It was shown numerically that the shape of the loading period, half-wave sine, a shape encountered during the tests, as well as the initial geometric imperfections have a great influence on the Dynamic Buckling of the shells. The relatively simple test set-up design to cause a shell to buckle Dynamically did not fulfill our expectations. Although, the process leading to eventually the Dynamic Buckling of the shell worked properly, still no test results were obtained to form a sound experimental database for this phenomenon. Based on the numerical predictions, correct guidelines were formulated for better test procedures to be applied in future tests, which will be reported in due time.
Chongmin Song - One of the best experts on this subject based on the ideXlab platform.
-
nonlinear Dynamic Buckling of the imperfect orthotropic e fgm circular cylindrical shells subjected to the longitudinal constant velocity
International Journal of Mechanical Sciences, 2018Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract In this study, an analytical approach on the nonlinear Dynamic Buckling of the orthotropic circular cylindrical shells made of exponential law functionally graded material (E-FGM) subjected to the longitudinal constant velocity is investigated with the incorporation of mercurial damping effect. The material properties are assumed to vary gradually in the thickness direction according to an exponential distribution function of the volume fraction of constituent materials. Theoretical formulations are derived based on improved Donnell shell theory (DST) and accounting for von-Karman strain–displacement relation, initial imperfection and damping effect. By applying Galerkin method and Airy's stress function, the obtained nonlinear differential equations are solved numerically by the fourth-order Runge–Kutta method. The nonlinear Dynamic stability of the orthotropic FG cylindrical shell is assessed based on Budiansky–Roth criterion. Additionally, a parametric study is conducted to demonstrate the effects of various velocities, initial imperfections, damping ratios, inhomogeneous parameters on nonlinear Dynamic Buckling behavior of an imperfect orthotropic FG cylindrical shell. Comparing results with those in other publications validates the proposed method.
-
nonlinear Dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by winkler pasternak elastic foundation subjected to a linearly increasing load
Journal of Sound and Vibration, 2018Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract This paper focuses on the Dynamic stability behaviors of the functionally graded (FG) orthotropic circular cylindrical shell surrounded by the two-parameter (Winkler-Pasternak) elastic foundation subjected to a linearly increasing load with the consideration of damping effect. The material properties are assumed to vary gradually in the thickness direction based on an exponential distribution function of the volume fraction of constituent materials. Equations of motion are derived from Hamilton's principle and the nonlinear compatibility equation is considered by the means of modified Donnell shell theory including large deflection. Then the nonlinear Dynamic Buckling equation is solved by a hybrid analytical-numerical method (combined Galerkin method and fourth-order Runge-Kutta method). The nonlinear Dynamic stability of the FG orthotropic cylindrical shell is assessed based on Budiansky-Roth criterion. Additionally, effects of different parameters such as various inhomogeneous parameters, loading speeds, damping ratios and aspect ratios and thickness ratios of the structure on Dynamic Buckling are discussed in details. Finally, the proposed method is validated with published literature.
-
nonlinear Dynamic stability analysis of euler bernoulli beam columns with damping effects under thermal environment
Nonlinear Dynamics, 2017Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:In this study, a unified nonlinear Dynamic Buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear Dynamic Buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for Dynamic Buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the Dynamic Buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural Dynamic Buckling behavior in the presence of damping effects under thermal environment are conducted.
-
nonlinear Dynamic characteristics and stability of composite orthotropic plate on elastic foundation under thermal environment
Composite Structures, 2017Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract An analytical computational scheme for nonlinear Dynamic characteristics and stability of an eccentrically composite orthotropic plate on Winkler-Pasternak elastic foundation subjected to different axial velocities is proposed with the incorporation of mercurial damping effects under thermal environment. Incorporating the classical plate theory and Von-Karman strain-displacement relation, the nonlinear compatibility equation is derived. The Galerkin method and Airy’s stress function are implemented to establish the nonlinear Dynamic Buckling equation accommodating the thermal and damping effects. Then the developed nonlinear differential equations are solved numerically by the fourth-order Runge-Kutta method. The characteristics of natural frequency, linear and nonlinear vibration, frequency-amplitude curve and nonlinear Dynamic responses are investigated by the developed approach with validations by other literatures. The nonlinear Dynamic Buckling loads are determined by using Budiansky-Roth criterion. Additionally, various effects of velocity, damping ratio, temperature change, Buckling mode, initial imperfection and foundation parameter on nonlinear Dynamic Buckling of the orthotropic plate are discussed.
Wei Gao - One of the best experts on this subject based on the ideXlab platform.
-
nonlinear vibration and Dynamic Buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on winkler pasternak elastic foundation
International Journal of Mechanical Sciences, 2018Co-Authors: Xiaojun Chen, Lei Liu, Wei GaoAbstract:Abstract The nonlinear vibration and the Dynamic Buckling of a graphene platelet reinforced sandwich functionally graded porous (GPL-SFGP) plate are thoroughly investigated in this paper. The investigated GPL-SFGP plate consists of two metal face layers and a functionally graded porous core with graphene platelet reinforcement. The effects of the Winkler–Pasternak elastic foundation, thermal environment and damping are incorporated. The open-cell metal foam model is implemented to model the mechanical properties of the porous core. Axial compressive stress is applied on the GPL-SFGP plate by exerting various compressive loading speeds at one edge of the plate. Grounded on the classical plate theory, both motion and geometric compatibility equations of the plate are deduced by introducing the Von Karman strain-displacement relationship and stress function. Both the Galerkin and the fourth-order Runge–Kutta methods are implemented to solve the governing equation of the Dynamic system. Meticulously designed numerical experiments are conducted to identify the critical influential factors of the Dynamic stability of the GPL-SFGP plate. The influences of loading speed, damping ratio, temperature variation, initial imperfection, elastic foundation parameters, porosity, GPL weight fraction and the dimensions of the GPL on the overall Dynamic stability of the GPL-SFGP plate are evidently demonstrated.
-
nonlinear Dynamic Buckling of the imperfect orthotropic e fgm circular cylindrical shells subjected to the longitudinal constant velocity
International Journal of Mechanical Sciences, 2018Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract In this study, an analytical approach on the nonlinear Dynamic Buckling of the orthotropic circular cylindrical shells made of exponential law functionally graded material (E-FGM) subjected to the longitudinal constant velocity is investigated with the incorporation of mercurial damping effect. The material properties are assumed to vary gradually in the thickness direction according to an exponential distribution function of the volume fraction of constituent materials. Theoretical formulations are derived based on improved Donnell shell theory (DST) and accounting for von-Karman strain–displacement relation, initial imperfection and damping effect. By applying Galerkin method and Airy's stress function, the obtained nonlinear differential equations are solved numerically by the fourth-order Runge–Kutta method. The nonlinear Dynamic stability of the orthotropic FG cylindrical shell is assessed based on Budiansky–Roth criterion. Additionally, a parametric study is conducted to demonstrate the effects of various velocities, initial imperfections, damping ratios, inhomogeneous parameters on nonlinear Dynamic Buckling behavior of an imperfect orthotropic FG cylindrical shell. Comparing results with those in other publications validates the proposed method.
-
nonlinear Dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by winkler pasternak elastic foundation subjected to a linearly increasing load
Journal of Sound and Vibration, 2018Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract This paper focuses on the Dynamic stability behaviors of the functionally graded (FG) orthotropic circular cylindrical shell surrounded by the two-parameter (Winkler-Pasternak) elastic foundation subjected to a linearly increasing load with the consideration of damping effect. The material properties are assumed to vary gradually in the thickness direction based on an exponential distribution function of the volume fraction of constituent materials. Equations of motion are derived from Hamilton's principle and the nonlinear compatibility equation is considered by the means of modified Donnell shell theory including large deflection. Then the nonlinear Dynamic Buckling equation is solved by a hybrid analytical-numerical method (combined Galerkin method and fourth-order Runge-Kutta method). The nonlinear Dynamic stability of the FG orthotropic cylindrical shell is assessed based on Budiansky-Roth criterion. Additionally, effects of different parameters such as various inhomogeneous parameters, loading speeds, damping ratios and aspect ratios and thickness ratios of the structure on Dynamic Buckling are discussed in details. Finally, the proposed method is validated with published literature.
-
nonlinear Dynamic stability analysis of euler bernoulli beam columns with damping effects under thermal environment
Nonlinear Dynamics, 2017Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:In this study, a unified nonlinear Dynamic Buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear Dynamic Buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for Dynamic Buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the Dynamic Buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural Dynamic Buckling behavior in the presence of damping effects under thermal environment are conducted.
-
nonlinear Dynamic characteristics and stability of composite orthotropic plate on elastic foundation under thermal environment
Composite Structures, 2017Co-Authors: Kang Gao, Wei Gao, Chongmin SongAbstract:Abstract An analytical computational scheme for nonlinear Dynamic characteristics and stability of an eccentrically composite orthotropic plate on Winkler-Pasternak elastic foundation subjected to different axial velocities is proposed with the incorporation of mercurial damping effects under thermal environment. Incorporating the classical plate theory and Von-Karman strain-displacement relation, the nonlinear compatibility equation is derived. The Galerkin method and Airy’s stress function are implemented to establish the nonlinear Dynamic Buckling equation accommodating the thermal and damping effects. Then the developed nonlinear differential equations are solved numerically by the fourth-order Runge-Kutta method. The characteristics of natural frequency, linear and nonlinear vibration, frequency-amplitude curve and nonlinear Dynamic responses are investigated by the developed approach with validations by other literatures. The nonlinear Dynamic Buckling loads are determined by using Budiansky-Roth criterion. Additionally, various effects of velocity, damping ratio, temperature change, Buckling mode, initial imperfection and foundation parameter on nonlinear Dynamic Buckling of the orthotropic plate are discussed.
M A Bradford - One of the best experts on this subject based on the ideXlab platform.
-
multiple unstable equilibrium branches and non linear Dynamic Buckling of shallow arches
International Journal of Non-linear Mechanics, 2014Co-Authors: Yonglin Pi, M A BradfordAbstract:Abstract An arch under a suddenly-applied load will oscillate about its equilibrium position. If the suddenly-applied load is sufficiently large, the oscillation may reach a position on the unstable equilibrium branch of the arch, triggering its Dynamic Buckling. In many cases, arches are supported by other structural members or by elastic foundations which provide elastic types of rotational restraints to the ends of the arch. When the rotational end restraints of an arch are not equal to each other, the in-plane non-linear equilibrium path of the arch may have multiple unstable branches, which will influence the Dynamic Buckling of the arch significantly. This paper investigates effects of multiple unstable equilibrium branches on the non-linear in-plane Dynamic Buckling of a shallow circular arch under a suddenly-applied central concentrated load. Two methods based on the energy approach are used to derive the Dynamic Buckling loads. It is found that the number and magnitude of Dynamic Buckling loads are influenced significantly by the number of unstable equilibrium branches, by the stiffness of the unequal rotational end restraints, and by the included angle and slenderness ratio of the arch.
-
nonlinear Dynamic Buckling of pinned fixed shallow arches under a sudden central concentrated load
Nonlinear Dynamics, 2013Co-Authors: M A BradfordAbstract:The structural behavior of a shallow arch is highly nonlinear, and so when the amplitude of the oscillation of the arch produced by a suddenly-applied load is sufficiently large, the oscillation of the arch may reach a position on its unstable equilibrium paths that leads the arch to buckle Dynamically. This paper uses an energy method to investigate the nonlinear elastic Dynamic in-plane Buckling of a pinned–fixed shallow circular arch under a central concentrated load that is applied suddenly and with an infinite duration. The principle of conservation of energy is used to establish the criterion for Dynamic Buckling of the arch, and the analytical solution for the Dynamic Buckling load is derived. Two methods are proposed to determine the Dynamic Buckling load. It is shown that under a suddenly-applied central load, a shallow pinned–fixed arch with a high modified slenderness (which is defined in the paper) has a lower Dynamic Buckling load and an upper Dynamic Buckling load, while an arch with a low modified slenderness has a unique Dynamic Buckling load.
-
Dynamic Buckling of shallow pin ended arches under a sudden central concentrated load
Journal of Sound and Vibration, 2008Co-Authors: M A BradfordAbstract:When a shallow arch is subjected to an in-plane load that is applied suddenly, the arch will oscillate about an equilibrium position due to the kinetic energy imparted to the arch by the sudden load. If the suddenly applied load is sufficient large, the motion of the arch may reach an unstable equilibrium position, leading to Dynamic Buckling of the arch. This paper presents a study of the Dynamic in-plane Buckling of a shallow pin-ended circular arch under a central radial load that is applied suddenly with infinite duration. The method of conservation of energy is used to establish the criterion for Dynamic Buckling of the shallow pin-ended arch and analytical solutions for the lower and upper Dynamic Buckling loads of the arch under this sudden central load with infinite duration are obtained. It is found that the Dynamic Buckling loads of a shallow pin-ended arch under a sudden central load with infinite duration are lower than its static Buckling loads, and that the Dynamic Buckling load increases with an increase of a dimensionless arch geometric parameter that is introduced. The effect of static preloading on the Dynamic Buckling of a shallow pin-ended arch is also investigated. It is found that the pre-applied static load decreases its Dynamic Buckling loads, but increases the sum of the pre-applied load and the Dynamic Buckling load.
