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During an earthquake and its effect, what happens on buildings is local damage and destruction which is different due to different characteristics such as diverse earthquake and geotechnical characteristic, different methods of analysis for earthquake-resistant structures, etc. Therefore, in addition to removing structural elements and their falling as debris, a shock and impulsive load could be added to the dynamic load imposed by the earthquake. Impact loads with extreme severity are loads with very low frequency of occurrence, but with extraordinary consequences. Undoubtedly appearing greater success in designing buildings resistant against extraordinary loads is required to forecast the real pattern and the impact of the impulsive loads. In other words, identify all possible failure modes of structures under extraordinary loads is necessary, which requires nonlinear analysis of structures under various loading conditions. Detailed modeling of the impact of an upper floor onto the floor below is feasible using current sophisticated nonlinear dynamic analysis software. Yet the computational effort in the case of large and complex structural systems can be excessive, especially if a detailed model of the whole structure is considered. Moreover, such analysis requires structural engineers with considerable expertise in nonlinear structural dynamics. Due to these limitations, detailed impact modeling is not practical for design applications. Hence, there is an evident need for simple, yet sufficiently accurate methodologies that can be used to establish whether the strength, ductility supply and energy absorption capacity of the lower impacted floor are adequate to withstand the imposed dynamic loads from the falling floor(s). This paper proposes a new design methodology for progressive collapse assessment of floor within multi-storey buildings subjected to impact from an above failed floor. The amount of debris and its scattering and distribution on different floors of a building play an important role in the operation of the impact load. The important point is that how these parameters should be considered in the dynamic analysis and how much the structure’s respond is sensitive to the impact characteristics such as impact velocity, the mass of debris and its distribution. This study has attempted to calculate the dynamic load factor (DLF) for samples of steel beams with an elastic-plastic behavior, and to extract the pattern of debris impact load in order to provide an equivalent loading pattern to estimate the performance of structures subjected to above failed floor(s). The study of dynamic load factors for the samples illustrates that the period of beam, the height of falling and the mass of debris have a noticeable effect on the result so that the DLF decreases by increasing in amount of the period of beams or the mass of debris, as well as it increases by increasing the height of falling. About the achieved patters for the impact load what is important is providing multi-line graphs in order to estimate the dynamic effect of the debris impact

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The investigation of failure modes of plates and behavior of various resistive structures to destructive effects of explosive waves, due to its importance in design of blast resistive structures, has been of interest to researchers for a long time. In this study, three different methods of numerical simulation of blast wave issues were carried out to evaluate and compare with the experimental results. As a consequence, by the means of study of clamped isotropic square plates under shock wave loading from various weight and distance of charges, the couple of ALE and ConWep methods were approved to have 8.54 per cent error in comparison with ALE and ConWep methods individually. Given that in the coupled approach and ConWep method, the equivalent weight of TNT for different types of explosives is needed, the equivalent weight of TNT for C4 was estimated by 1.14, and according to the empirical pressure-time chart and empirical equation for pressure in the air, this coefficient was proved to be right and the pressure and impulse charts for TNT and C4 explosives with the same weights was studied.

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In this paper, a new formulation is developed for nonlinear dynamic analysis of 2-D truss structures. This formulation is based on dynamics of co-rotational 2-D truss. The idea of co-rotational approach is to separate rigid body motions from pure deformations at the local element level. Using this approach, internal force vector and tangent stiffness matrix, inertia force vector and the tangent dynamic matrix are derived. Furthermore, the inertia force vector, tangent dynamic matrix, mass matrix and gyroscopic matrix are directly derived from the derivation of current orientation matrix with respect to global displacements or orientation matrixes. Using this new formulation, nonlinear response of any 2-D truss structures can be examined. Here, for example the response of tensegrity structures under dynamic loads are investigated. Tensegrity structures are a class of structural system composed of cable (in tension) and strut (in compression) components with reticulated connections, and assembled in a self-balanced fashion. These structures have nonlinear behaviour due to pre-stress forces. And their integrity is based on a balance between compression and tension. Two numerical examples are presented to illustrate the new formulation and results show that the new formulation has more convergence rate than the existing models.

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This paper presents the investigation of general formulation and numerical solution of the dynamic load carrying capacity (DLCC) of flexible link manipulator. The proposed method is based on open loop optimal control problem. A two point boundary value problem (TPBVP) is provided, extracted from the Pontryagin's minimum principle. The indirect approach is employed to derive optimality conditions. The system’s dynamics equation of motion is obtained from Gibbs-Appell (G-A) formulation and assumed mode method (AMM). Elastic properties of the links are modeled according to the assumption of Timoshenko beam theory (TBT) and its associated mode shapes. As TBT is more accurate compared with the Euler-Bernoulli beam theory, it is exploited for mathematical modeling of flexible links. The main contribution of the paper is to calculate the maximum allowable load of a flexible link robot while an optimal trajectory is provided. Finally, the result of the simulation and experimental platform are compared for a two-link flexible arm to verify the introduced technique. The efficiency of the proposed method is illustrated by performing some simulation studies on the IUST flexible link manipulator. Simulation and experimental results confirm the validity of the claimed capability for controlling point-to-point motion of the proposed method and its application toward DLCC calculation.

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Offshore platforms are exposed to random cyclic loads imposed on the structure by natural phenomena including waves, sea currents, wind and etc, so fatigue analysis of these structures is one of the most important design steps. Hot spot method is one of the most common techniques for evaluating of the fatigue life of offshore platforms. In this approach, the stress adjacent to the weld is estimated by extrapolation from the stress distribution approaching the weld, as obtained by finite element method or perhaps from strain measurements on the surface. In order to calculate the fatigue life of Amir Kabir semi-submersible drilling platform, first a model of platform is created. Then according to the environmental conditions of the Caspian sea, hydrodynamic forces exerted on the platform are calculated. The simulated hydrodynamic forces are then applied to the platform structure for calculating the stress and strain fields in the whole structure. It is found that the intersection of column and pontoon is the critical section of the platform and hence the fatigue life of the structure is predicted in terms of conditions of this location.

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In this paper, the behavior of copper and steel rectangular plates with clamped boundary conditions subjected to underwater explosion loading is investigated. Cavitation is a phenomenon that occurs in this process. During the cavitation, the total pressure of the explosion becomes zero, so that the governing equations of motion time will be different before and after the cavitation. As a result, in terms of analysis and design, the cavitation time is significant in studying the behavior of a rectangular plate at underwater explosive loading. To calculate the cavitation time, the equations of motion of a rectangular plate underwater explosive loading are derived first, based on Hamilton principle and variation method. Then, in order to obtain the forced response of the rectangular plate, the exact free vibration solution of the rectangular plate is derived for exact mode shapes. Then, the speed and generated stress of plate during cavitation time are calculated and compared with the yield stress of copper and steel rectangular plates. Using this method, one can distinguish the cavitation with in the elastic or plastic regimes. Results show that the cavitation time is on the order of microsecond.

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Nowadays, availability, durability, reliability, weight and strength, as the most important factors in optimum engineering design, are responsible for the widespread application of plates in the industry. Buckling in the elastic or elastoplastic regim is one of the phenomena that can be occurred in the axial compressive loading. Using Galerkin method on the basis of trigonometric shape functions, the elastoplastic dynamic buckling of a thin rectangular plate with different boundary conditions subjected to compression exponetiail pulse functions is investigated in this paper. Based on two theories of plasticity: deformation theory of plasticity (DT) with Hencky constitutive relations and incremental theory of plasticity (IT) with Prandtl-Reuss constitutive relations the equilibrium, stability and dynamic elastoplastic buckling equations are derived. Ramberg-Osgood stress-strain model is used to describe the elastoplastic material property of plate. The effects of symmetrical and asymmetrical boundary conditions, geometrical parameters of plate, force pulse amplitude, and type of plasticity theory on the velocity and deflection histories of plate are investigated. According to the dynamic response of plate the results obtained from DT are lower than those predicted through IT. The resistance against deformation for plate with clamped boundary condition is more than plate with simply supported boundary condition. Consequently, the adjacent points to clamped boundary condition have a lower velocity field than adjacent points to simply supported boundary condition.

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In this paper, numeral and experimental analysis of composite metal vessel is investigated under variable pressure loading. For this purpose, a sample of multi section cylindrical vessel is considered. The pizo electric 1000 bars sensors are used to measure pressure. The sensors are installed in the holes on the metal cylindrical vessel. The amplification parts are used to adjust sensors. The test is done under dynamic loading. The results are recorded by data logers in pressure-time chart. The aim of this study is to optimize the weight and strength of the vessel with using trial and error by numeral analysis inverse explosive loading. In order to, a sample of multi section cylindrical vessel is analyzed with abaqus finite element software. The load in the vessel is derived by charts from experimental tests. The load obtained from experimental tests as a dynamic load is analyzed and compared with metal vessel and metal- Composite vessel. The results obtained from abaqus finite element software have discussion in different case. Finally, geometric and material properties of liner and composite is suggested for optimize the weight and strength of the vessel.

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Mechanical behavior of articular cartilage is affected by many factors. Inhomogeneous distribution of proteoglycans and collagen fibers through the thickness causes some depth-wise behavior. Mechanical properties directly affect stress and deformation of the tissue. In previous studies complexities and variation in mechanical properties were ignored. The aim of the present study is to create a model close to real anatomy of articular cartilage in knee joint and to simulate its behavior under dynamic gate in the stance phase. A 3D finite element (FE) model was created. It was constructed considering femur and tibial cartilages as well as medial and lateral meniscus. In the FE model, a nonlinear isotropic viscoelastic material model used for cartilages and a linear anisotropic elastic one was chosen for meniscuses. As well, cartilages assumed saturated . Numerical simulations on the model showed that peak of maximum principal stress occurred in superficial layer. It was decreased through thickness. These expressed why osteoarthritis fall out in the exterior layers such superficial . The present study showed that hydraulic permeability variation in cartilage as a strain-dependent variable was negligible in dynamic loading. Also, results had a good agreement with experimental ones

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The dynamic stability of single-walled carbon nanotubes (SWCNT) and double-walled carbon nanotubes (DWCNT) embedded in an elastic medium subjected to combined static and periodic axial loads are investigated using Floquet–Lyapunov theory and bounded solution theory. An elastic Euler- Bernoulli beam model is utilized in which the nested slender nanotubes are coupled with each other through the van der Waals (vdW) interlayer interaction. The Galerkin’s approximate method on the basis of trigonometric mode shape functions is applied to reduce the coupled governing partial differential equations to a system of the extended Mathieu-Hill equations. Applying Floquet–Lyapunov theory and Rung-Kutta numerical integration method with Gill coefficients, the influences of number of layer, elastic medium, exciting frequency and combination of exciting frequency on the instability conditions of SWCNTs and DWCNTs are investigated. A satisfactory agreement can be observed by comparison between the predicted results of Floquet–Lyapunov theory with bounded solutions theory ones. Based on results, increasing the number of layers, and elastic medium, dynamic stability of SWCNTs and DWCNTs surrounding elastic medium increase. Moreover, the instability of CNTs increases by increasing the exciting frequency.

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In this paper, a novel model based on the indicial functions concept is presented to calculate the unsteady aerodynamic loads in the incompressible and subsonic compressible flow. Indicial functions represent the two-dimensional airfoil response to a unit step change in the angle of attack or the pitch rate about the reference axis. In contrast to the incompressible flow where the aerodynamic loads can be determined in terms of a single indicial function, four indicial aerodynamic functions are required to find them in the compressible one. If the indicial functions are known, the unsteady loads can then be obtained through the superposition of indicial responses using Duhamel’s integral for any arbitrary motion. For the purpose of combination the aerodynamic loads for the entire subsonic flow speed range, i.e. 0≤M≤0.8, a new, efficient and Mach dependent approximations of the indicial functions are presented by using the analytical as well as numerical data. Using four instead of seven Mach dependent coefficients in the common indicial functions, the required coefficient are decreased from 28 to 16 to fully describe the aerodynamic loads. Utilizing the indicial functions, then a novel and convenient form of unsteady aerodynamic loads and the corresponding state-space representation is presented; having a unified formulation in incompressible and subsonic compressible flight speed regimes. Based on the strip theory as well as the modified lift curve slope, the finite span effect of 3D wings is also included. The generated indicial functions is validated against available results, which shows a good agreement.

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In this paper, numerical and analytical solution of composite metal cylindrical vessel are investigated under dynamic load using first-order shear deformation theory and differential quadrature method. For this purpose, the shell equilibrium equations are derived based on the first order shear deformation theory. The load applied to the shell is achieved from the experimental test of a double-base propellant and then, is applied to the model in numerical and theoretical analysis. The aim of this paper is study and investigate the behavior of the composite metal cylindrical vessel under dynamic load with first-order shear deformation theory and comparing its results with the numerical solution. Therefore, after extracting the shell equilibrium equations are used from differential quadrature method for solve the equations. Then, the governing equations are extracted in a composite metal cylindrical vessel to form the matrix equations to solve with differential quadrature method. To apply boundary conditions from free and support clamping conditions are used and the results of these two modes are compared together. The MATLAB programming code is used to solve differential quadrature equations. To validate theoretical results, modeling and numerical analysis done by Abaqus finite element software and then, results are compared with the analytical solution using the differential quadrature method.

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Designing explosion of gas pipelines, gun tubes, pulse detonation engine tubes and etc, all related to problem of cylindrical shell subjected to dynamic internal loads. In this paper, dynamic response of the thick cylindrical shell subjected to dynamic internal load with considering the high order shear deformation theory (HODT) is investigated and compared with the first order shear deformation theory of Mirsky- Hermann (FSDT). The effects of transverse shear deformation and rotatory inertia were included in the governing equations of the dynamic system. First, the equations of motion have been derived by using Hamilton’s principle then by changing variables the obtained partial differential equations have been converted to ordinary differential equations. With this method, the problem can be solved for various mechanical moving pressure loads without considering the effect of boundary conditions with long length assumption. The results of the present analytical method have been verified by comparing with finite element results, by using software. The comparison of the results with the finite element method shows that the high order theory and first order Mirsky-Hermann theory can predict the dynamic response of the thick cylindrical shell and the high order theory in areas away from the middle layer is more successful.

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Composite tubes may be subjected to impact loads during placement or operation. By determining the impact properties of composite tubes and using them in the design process, the accuracy of the behavior of these structures in the loading condition is guaranteed. In this study, the behavior of glass/epoxy composite tubes under dynamic axial loading was experimentally investigated. Also, the effects of parameters such as fiber density, fiber alignment angle, internal diameter of the tube and impact energy on the amount of pipe damage were also studied. To prepare composite specimens, E-type glass fiber was used with two different densities of 200 gr⁄m^2 and 400 gr⁄m^2 . The specimens were placed on a drop weight machine of Tafresh University by a fixture, and the Impactor was released from the height of 2 meters. The force -displacement diagrams for each test were extracted and compared with each other. Also, a parameter called specific energy absorption was calculated for all samples in order to compare the efficiency of the samples as energy absorber. The results of this study showed that increasing the fiber density, number of layers and diameter of the tube increases the specific energy absorption. It was also observed that with the increase of the axial dynamic impact energy, the mechanical properties of the specimen will be changed and the specimen will be firmly established.

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The loading rate and specimen size are two main influential factors which control the tensile and compressive strengths of Quasi-brittle materials such as concrete, ceramic and rock. Most of the studies in the past have been focused on the size effect in the static loading situations i.e. in situations in which the effect of the loading rate and inertia can be ignored. In particular, fracture mechanics size effect have received substantial attention both with respect to the physical testing and the numerical modeling. On the other hand, combined effect of the specimen size and loading rate on the rock strength has received little attention in the literature. Understanding the dynamic size effect of Quasi-brittle materials such as rock is essential for better analysis and design of rock structures. This is particularly the case when rock is subjected to the blasting loads or when it is prone to the strain bursting. Studies on the failure of rock under the coupled effect of specimen size and loading rate are far from sufficient. Due to the limitations of the laboratory test devices, limited research efforts have been conducted on the size effect of materials under dynamic loading. In this study, a 3D hybrid finite-discrete element code called CA3 was used to simulate the Split Hopkinson Pressure Bar test. The Incident and Transmitted bars were modeled by the finite element method while the Brazilian specimen was simulated using a Bonded Particle Model (BPM). The bars were assumed to beave elastically while the simulated specimen could develop micro and macro cracks which eventually could end up to complete disintegration and failure. Brazilian specimens with different sizes were numerically modeled. The specimen contained a vertical notch so that fracture mechanics size effect under high strain loading rate could be studied. The samples were subjected to different loading rate by adjusting the incoming wave in the incident bar. A micromechanical model in which the contact bond strength was allowed to vary in proportion to the relative velocity at the contact point of the involved particles was employed to capture the loading rate effect. The effect of sample size on the dynamic tensile strength of rock was explored and compared with the static size effect. The results were analyzed and discussed using the dimensional analysis approach. The numerical results suggest that the dynamic size effect on tensile strength of rock is different from the static size effect. While for small loading rates, the rock strength reduces as the specimen size increases, this is not the case when high loading rates are involved. For high loading rates, with the increase in the specimen size, the tensile strength initially increases. However, with further increase in the specimen size and the increase in the distance between the notch tips and the impact points, it appears that the inertia and loading rate effects reach to a stable situation, i.e. with further increase in the specimen size, the material strength remains constant. This interesting observation is discussed and compared with the published data in the literature.

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In mechanics of rock fracture and comminution, researchers have always been looking for a relationship between the consumed energy and the particle size distribution of the disintegrated rock specimen. This relationship has important industrial applications considering the fact that comminution of rock is a very energy demanding process and its efficiency is very low. Furthermore, investigating the damage evolution of rock under different loading rates, helps to better understand and more accurately design rock structures such as tunnels, rock slopes and foundations subjected to dynamic loading. In this work, a hybrid finite-discrete element numerical model was used to simulate rock disintegration under different loading rates in the Split Hopkinson Pressure Bar (SHPB) system. The rock and the steel bars in the SHPB apparatus were simulated by the Bonded Particle Model (BPM) and finite element model, respectively. BPM is a simplified version of the discrete element method in which the discrete particles are spherical in shape. Spherical particles or balls in the BPM are very useful in reducing the computational time; the contact detection of the spherical particles is computationally very fast. The computer program CA3, which is a 3D code for static, dynamic and nonlinear simulation of geomaterials was used for the numerical analysis. To capture the rate dependent behavior of rock, a micromechanical model was utilized in which the bond strength at a contact point increases as a function of relative velocity of involved particles. The numerical model was calibrated to mimic the mechanical behavior of Masjed Soleyman sandstone. To facilitate and expedite the calibration process of the BPM system, the curves and dimensionless parameters introduced in the literature were used. Input pulses with different intensities were applied to the specimen in the numerical modeling of the SHPB system. The input energy and the energy consumed to disintegrate the numerical rock specimen were evaluated by the numerical integration. Different particle sizes in the BPM system were used to investigate the impact of combined particle size and input energy on the rock disintegration. The results suggest that the energy consumption density for rock crushing changes linearly with the stress rate. Furthermore, it is shown that the dynamic strength of the rock increases with the increase in the consumed energy density. The disintegrated numerical specimen was carefully inspected and its particle size distribution was obtained. This was achieved by using a searching algorithm to identify the clusters in the damaged specimen; each cluster was made of one or several spherical particles. The volume of each cluster was calculated by finding the volume of its constituent particles and the porosity of the specimen. This volume was used to obtain the equivalent radius of the cluster; the cluster shape was imagined as a sphere to identify the equivalent particle or cluster size. The mean particle size (D50) of the damaged numerical specimen shows a linear relationship with the stress rate in a logarithmic coordinate system, which is consistent with the physical test results reported in the literature.