In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).展开更多
The static test of 13 square hollow section(SHS) X-joints with different β and different types of plate reinforcement under in-plane moment in brace was carried out. Experimental test schemes, failure modes of specim...The static test of 13 square hollow section(SHS) X-joints with different β and different types of plate reinforcement under in-plane moment in brace was carried out. Experimental test schemes, failure modes of specimens, moment-vertical displacement curves, moment-deformation of the chord, and strain strength distribution curves were presented. The effect of β and plate reinforcement types on in-plane flexural property of SHS X-joints was studied. Results show that punching shear of chord face disappears, brace material fracture appears and concave and convex deformation of chord decrease when either collar plates or doubler plates were welded on chord face. Moment-vertical displacement curves of all specimens have obvious elastic, elastic-plastic and plastic stages. As β increases, the in-plane flexural ultimate capacity and initial stiffness of joints of the same plate reinforcement type increase, but ductility of joints decreases. With the same β, the in-plane flexural initial stiffness and ultimate capacity of doubler plate reinforced joints, collar plate reinforced joints, and unreinforced joints decrease progressively. Thickness of reinforcement plate has no obvious effect on in-plane flexural initial stiffness and ultimate capacity of joints. As thickness of reinforcement plate increases, the ductility of reinforced X-joints decreases. The concave and convex deformation of every specimen has good symmetry;as β increases, the yield and ultimate deformation of chord decrease.展开更多
This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stres...This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Appling the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.展开更多
Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material (FGM) circular plates with in- plane elastic restraints under transversely non-uniform tem...Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material (FGM) circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.展开更多
Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electri...Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.展开更多
The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. T...The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson's ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.展开更多
Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or pa...Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.展开更多
The paper describes the simulation of impact loads applied on plate panels with welding-induced residual stresses and deformation (WSD). Numerical simulations using FEM are carried out to study the influence of weldin...The paper describes the simulation of impact loads applied on plate panels with welding-induced residual stresses and deformation (WSD). Numerical simulations using FEM are carried out to study the influence of welding-induced residual stresses and deformation on the impact strength of plate panels. Welding is simulated using a three dimensional thermal mechanical coupled finite element method. The welding stress and deformation are taken as the initial imperfections in the impact strength analysis and their influence on the behavior of plate panels subjected to impact loadings. The impact loadings from the three directions, the lateral direction and two in-plane directions of the plate panels are studied. Results show a certain reduction in the impact strength due to the existence of welding stress and deformation in the plate panels. It is found that the reduction of impact force is strongly influenced by the welding deformation and the impact directions in the plate panels. This reduction is more significant when the impact force is in the lateral direction.展开更多
Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is app...Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is applied to measure the out-of-plane deformation of structures with one-shot projection.Through color fringe recognizing,decoding and triangulation processing for the captured images corresponding to each deformation state,the feasibility of the method is testified by the measurement of elastic deflections of a flexible square plate,showing good agreement with those from the calibrated displacement driver.The plastic deformation of two alloy aluminum rectangular tubes is measured to show the technique application to surface topographic evaluation of the buckling structures with large displacements.展开更多
A full-scale composite floor plate was tested to investigate the flexural behavior and in-plane effects of the floor slab in a grillage of composite beams that reduces the tendency for longitudinal splitting of the co...A full-scale composite floor plate was tested to investigate the flexural behavior and in-plane effects of the floor slab in a grillage of composite beams that reduces the tendency for longitudinal splitting of the concrete slab along the line of the primary beams. This is important in cases where the steel decking is discontinuous when it is orientated parallel to the beams. In this case, it is important to demonstrate that the amount of transverse reinforcement required to transfer local forces from the shear connectors can be reduced relative to the requirements of Eurocode 4. The mechanism under study involved in-plane compression forces being developed in the slab due to the restraining action of the floor plate, which was held in position by the peripheral composite beams;while the secondary beams acted as transverse ties to resist the forces in the floor plate that would otherwise lead to splitting of the slab along the line of the primary beams. The tendency for cracking along the center line of the primary beam and at the peripheral beams was closely monitored. This is the first large floor plate test that has been carried out under laboratory conditions since the Cardington tests in the early 1990s, although those tests were not carried out to failure. This floor plate test was designed so that the longitudinal force transferred by the primary beams was relatively high (i.e., it was designed for full shear connection), but the transverse reinforcement was taken as the minimum of 0.2% of the concrete area. The test confirmed that the primary beams reached their plastic bending resistance despite the discontinuous decking and transverse reinforcement at the minimum percentage given in Eurocode 4. Based on this test, a reduction factor due to shear connectors at edge beams without U-bars is proposed.展开更多
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).
基金Projects(51278209 and 51478047) supported by the National Natural Science Foundation of ChinaProject(ZQN-PY110) supported by Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University,China+1 种基金Project(2014FJ-NCET-ZR03) supported by Program for New Century Excellent Talents in Fujian Province University,ChinaProject(JA13005) supported by Incubation Programme for Excellent Young Science and Technology Talents in Fujian Province Universities,China
文摘The static test of 13 square hollow section(SHS) X-joints with different β and different types of plate reinforcement under in-plane moment in brace was carried out. Experimental test schemes, failure modes of specimens, moment-vertical displacement curves, moment-deformation of the chord, and strain strength distribution curves were presented. The effect of β and plate reinforcement types on in-plane flexural property of SHS X-joints was studied. Results show that punching shear of chord face disappears, brace material fracture appears and concave and convex deformation of chord decrease when either collar plates or doubler plates were welded on chord face. Moment-vertical displacement curves of all specimens have obvious elastic, elastic-plastic and plastic stages. As β increases, the in-plane flexural ultimate capacity and initial stiffness of joints of the same plate reinforcement type increase, but ductility of joints decreases. With the same β, the in-plane flexural initial stiffness and ultimate capacity of doubler plate reinforced joints, collar plate reinforced joints, and unreinforced joints decrease progressively. Thickness of reinforcement plate has no obvious effect on in-plane flexural initial stiffness and ultimate capacity of joints. As thickness of reinforcement plate increases, the ductility of reinforced X-joints decreases. The concave and convex deformation of every specimen has good symmetry;as β increases, the yield and ultimate deformation of chord decrease.
文摘This paper presents a simple solution of the dynamic buckling of stiffened plates under in-plane impact loading. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Appling the Hamilton's principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained form Budiansky-Roth criterion.
基金Project supported by the National Natural Science Foundation of China(Nos.11272278 and11672260)the China Postdoctoral Science Foundation(No.149558)
文摘Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material (FGM) circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.
基金Project (Nos. 10172003 and 10372003) supported by the NationalNatural Science Foundation of China
文摘Study of generalized plane strain has so far been limited to elasticity. The present is aimed at parallel development of transversely isotropic piezoelasticity. By assuming that the along depth distribution of electric potential is linear, and that com- monly used Kane-Mindlin kinematical assumption is valid, two dimensional solution systems were deduced, for which, explicit solutions of the out-of-plane constraint factor, as well as the stress resultant concentration factor around a circular hole in a transversely isotropic piezoelectric plate subjected to remote biaxial tension are obtained. Comparisons of these formulas with their counterparts for elastic case yielded suggestions that whether the piezoelectric effect exacerbates or mitigates the stress resultant concentration greatly depends on material properties, particularly, the piezoelectric coefficients; the effect of plate thickness was extensively investigated.
基金Project supported by the National Natural Science Foundation of China (No. 11072177)
文摘The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson's ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB026103)the National Natural Science Foundation of China(Grant No.51009136)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011212)
文摘Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.
文摘The paper describes the simulation of impact loads applied on plate panels with welding-induced residual stresses and deformation (WSD). Numerical simulations using FEM are carried out to study the influence of welding-induced residual stresses and deformation on the impact strength of plate panels. Welding is simulated using a three dimensional thermal mechanical coupled finite element method. The welding stress and deformation are taken as the initial imperfections in the impact strength analysis and their influence on the behavior of plate panels subjected to impact loadings. The impact loadings from the three directions, the lateral direction and two in-plane directions of the plate panels are studied. Results show a certain reduction in the impact strength due to the existence of welding stress and deformation in the plate panels. It is found that the reduction of impact force is strongly influenced by the welding deformation and the impact directions in the plate panels. This reduction is more significant when the impact force is in the lateral direction.
文摘Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is applied to measure the out-of-plane deformation of structures with one-shot projection.Through color fringe recognizing,decoding and triangulation processing for the captured images corresponding to each deformation state,the feasibility of the method is testified by the measurement of elastic deflections of a flexible square plate,showing good agreement with those from the calibrated displacement driver.The plastic deformation of two alloy aluminum rectangular tubes is measured to show the technique application to surface topographic evaluation of the buckling structures with large displacements.
基金part of a collaborative project between the Steel Construction Institute, the University of Stuttgart, the University of Luxembourg, Arcelor Mittal S.A., and the University of Bradford funded by the European Community’s Research Fund for Coal and Steel (RFSR-CT-2012-00030)
文摘A full-scale composite floor plate was tested to investigate the flexural behavior and in-plane effects of the floor slab in a grillage of composite beams that reduces the tendency for longitudinal splitting of the concrete slab along the line of the primary beams. This is important in cases where the steel decking is discontinuous when it is orientated parallel to the beams. In this case, it is important to demonstrate that the amount of transverse reinforcement required to transfer local forces from the shear connectors can be reduced relative to the requirements of Eurocode 4. The mechanism under study involved in-plane compression forces being developed in the slab due to the restraining action of the floor plate, which was held in position by the peripheral composite beams;while the secondary beams acted as transverse ties to resist the forces in the floor plate that would otherwise lead to splitting of the slab along the line of the primary beams. The tendency for cracking along the center line of the primary beam and at the peripheral beams was closely monitored. This is the first large floor plate test that has been carried out under laboratory conditions since the Cardington tests in the early 1990s, although those tests were not carried out to failure. This floor plate test was designed so that the longitudinal force transferred by the primary beams was relatively high (i.e., it was designed for full shear connection), but the transverse reinforcement was taken as the minimum of 0.2% of the concrete area. The test confirmed that the primary beams reached their plastic bending resistance despite the discontinuous decking and transverse reinforcement at the minimum percentage given in Eurocode 4. Based on this test, a reduction factor due to shear connectors at edge beams without U-bars is proposed.