A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circu...A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.展开更多
A simplified analytical solution suitable for simple stacking sequences was developed using the Euler buck- ling theory, the structure＇s equations of equilibrium and laminate panel mathematical formulation. Comparing...A simplified analytical solution suitable for simple stacking sequences was developed using the Euler buck- ling theory, the structure＇s equations of equilibrium and laminate panel mathematical formulation. Comparing these results with numerical results reveals the accuracy of the method and even more, allows us to validate the nu- merical analysis. Therefore, two important results are obtained： a simplified analytical solution for the buckling problem and validation of the numerical results. Another important and novel finding is related to the influence of the angle ply orientation and of the cutouts, on the buckling load. Under symmetrical boundary conditions and loading case, rectangular panels with elliptical cutouts, give better results for 90~ oriented plies than for 0 oriented ones. With a compression load applied in the X direction, and with material properties 10 times better in X direction than in Y direction, the best results are obtained when the load is aligned with the Y direction associated to the ma- terial reference frame. Moreover, panels with cutouts seem to behave better than panels without cutouts under cer- tainply orientation angles.展开更多
Cutouts are often provided in composite structural components for practical reasons. For instance, aircraft components such as wingspar, fuselage and ribs are provided with cutouts for access, inspection, fuel lines a...Cutouts are often provided in composite structural components for practical reasons. For instance, aircraft components such as wingspar, fuselage and ribs are provided with cutouts for access, inspection, fuel lines and electric lines or to reduce the overall weight. This paper addresses the effect of boundary condition on buckling and postbuckling responses, failure loads, and failure characteristics of composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) and having different lay-ups under in-plane shear (positive and negative) load, using finite-element method. The FEM formulation is based on the first order shear deformation theory in conjunction with geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the effect of boundary condition on buckling, first-ply failure and ultimate failure loads of a quasi-isotropic laminate with cutout is more for positive shear load than that for the negative shear load for almost all cutout shapes. It is also noted that under in-plane shear loads postbuckling stiffness of (0/90)4s laminate with circular cutout is maximum, while it is minimum for (45/—45)4s laminate with circular cutout, irrespective of boundary conditions.展开更多
Gasturbines are provided with cut-outs for minimizing vibrations. Round cut-outs are usually favored but there are various designs which offer more advantages over the circular shape. The objective of this work was to...Gasturbines are provided with cut-outs for minimizing vibrations. Round cut-outs are usually favored but there are various designs which offer more advantages over the circular shape. The objective of this work was to compare stress reduction during the induced vibration in the hollow gas turbine shafts by introducing different cut-outs. Round, square and elliptical cut-outs under different orientations were compared. It is observed that a square cutout at 45°?orientation has the least stress concentration. This is due to the effective orientation of plastic strains along the principal axis.展开更多
Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite element method is use...Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite element method is used.The volume fraction of the material constituents is assumed to follow a simple power law distribution.The parameters considered in this paper are as follows：cutout size,cutout location,number of cutouts and different boundary conditions.It should be mentioned that free vibration for FG plates（such as rectangular？skew？trapezoidal？circular plates） with multiple cutouts has not been studied yet and hence the results out coming from this paper may be used as bench marks for future works.展开更多
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
Stresses, particularly those at geometric discontinuities, influence the structural integrity of engineering components. Motivated by the prevalence of complicated-shaped perforated components, the objective of this p...Stresses, particularly those at geometric discontinuities, influence the structural integrity of engineering components. Motivated by the prevalence of complicated-shaped perforated components, the objective of this paper is to demonstrate the ability to stress analyze loaded finite members containing asymmetrical, irregularly-shaped cutouts. Recognizing the difficulties in obtaining purely theoretical or numerical solutions for these situations, the paper presents an expeditious means of experimentally stress analyzing such structures. Processing the load-induced temperature information with a series representation of a stress function provides the independent stress components reliably full-field, including on the edge of a hole. The stresses satisfy equilibrium and strains satisfy compatibility. In addition to being able to stress analyze complicated shapes using real, rather than complex variables, the technique is significant in which it smooths the recorded thermal information, is widely applicable, and requires neither differentiating the measured data nor knowing the elastic properties or external boundary conditions. The latter is extremely important since the external loading is often unknown in practice. That the approach provides the independent stresses is also significant since fatigue analyses and strength criteria typically necessitate knowing the individual components of stress. Present results are supported by those from a finite element analysis, strain gage measurements and load equilibrium.展开更多
The perforated stiffened panel is generally found as a sub-component of sophisticated structures.The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental condi...The perforated stiffened panel is generally found as a sub-component of sophisticated structures.The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental conditions.Hence,an accurate knowledge of critical buckling behaviour of stiffened panels is very much essential for a reliable and lightweight structural design.In this paper,the focus is on quasi-laminated panels with different cutout shapes of various sizes and their responses to hygrothermal environments under nonlinearly varying edge loads and is compared with the locally stiffened panels.Towards this,the modelling of the panel and stiffener is done by adopting nine-noded heterosis plate elements and three noded beam elements respectively.The stiffener formulation is suitably modified in order to take the torsional effect also into consideration along with the effect of shear deformation.Initially,the plate and the stiffener elements are treated separately,and then the displacement compatibility is maintained between them by using the transformation matrix.For a given loading and geometric discontinuity,the stress distribution within the perforated panel is highly non-uniform in nature and hence a dynamic approach has been used to calculate buckling loads by adopting two sets of boundary conditions,one set for pre-buckling stress analysis and the second set for buckling analysis.Four different quasi-isotropic stacking sequences are deliberated in this work by varying different ply-orientation in each scheme.The study also addresses the effect of various parameters such as nonlinear loads,hygro-thermal loads,cutout size and shapes,position of cutout,stiffener parameters,stacking sequences,thickness of plate and boundary conditions.展开更多
基金The work was supported by the National Natural Science Foundation of China (Grant No. 100Tz064) .
文摘A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.
文摘A simplified analytical solution suitable for simple stacking sequences was developed using the Euler buck- ling theory, the structure＇s equations of equilibrium and laminate panel mathematical formulation. Comparing these results with numerical results reveals the accuracy of the method and even more, allows us to validate the nu- merical analysis. Therefore, two important results are obtained： a simplified analytical solution for the buckling problem and validation of the numerical results. Another important and novel finding is related to the influence of the angle ply orientation and of the cutouts, on the buckling load. Under symmetrical boundary conditions and loading case, rectangular panels with elliptical cutouts, give better results for 90~ oriented plies than for 0 oriented ones. With a compression load applied in the X direction, and with material properties 10 times better in X direction than in Y direction, the best results are obtained when the load is aligned with the Y direction associated to the ma- terial reference frame. Moreover, panels with cutouts seem to behave better than panels without cutouts under cer- tainply orientation angles.
文摘Cutouts are often provided in composite structural components for practical reasons. For instance, aircraft components such as wingspar, fuselage and ribs are provided with cutouts for access, inspection, fuel lines and electric lines or to reduce the overall weight. This paper addresses the effect of boundary condition on buckling and postbuckling responses, failure loads, and failure characteristics of composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) and having different lay-ups under in-plane shear (positive and negative) load, using finite-element method. The FEM formulation is based on the first order shear deformation theory in conjunction with geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the effect of boundary condition on buckling, first-ply failure and ultimate failure loads of a quasi-isotropic laminate with cutout is more for positive shear load than that for the negative shear load for almost all cutout shapes. It is also noted that under in-plane shear loads postbuckling stiffness of (0/90)4s laminate with circular cutout is maximum, while it is minimum for (45/—45)4s laminate with circular cutout, irrespective of boundary conditions.
文摘Gasturbines are provided with cut-outs for minimizing vibrations. Round cut-outs are usually favored but there are various designs which offer more advantages over the circular shape. The objective of this work was to compare stress reduction during the induced vibration in the hollow gas turbine shafts by introducing different cut-outs. Round, square and elliptical cut-outs under different orientations were compared. It is observed that a square cutout at 45°?orientation has the least stress concentration. This is due to the effective orientation of plastic strains along the principal axis.
文摘Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite element method is used.The volume fraction of the material constituents is assumed to follow a simple power law distribution.The parameters considered in this paper are as follows：cutout size,cutout location,number of cutouts and different boundary conditions.It should be mentioned that free vibration for FG plates（such as rectangular？skew？trapezoidal？circular plates） with multiple cutouts has not been studied yet and hence the results out coming from this paper may be used as bench marks for future works.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
文摘Stresses, particularly those at geometric discontinuities, influence the structural integrity of engineering components. Motivated by the prevalence of complicated-shaped perforated components, the objective of this paper is to demonstrate the ability to stress analyze loaded finite members containing asymmetrical, irregularly-shaped cutouts. Recognizing the difficulties in obtaining purely theoretical or numerical solutions for these situations, the paper presents an expeditious means of experimentally stress analyzing such structures. Processing the load-induced temperature information with a series representation of a stress function provides the independent stress components reliably full-field, including on the edge of a hole. The stresses satisfy equilibrium and strains satisfy compatibility. In addition to being able to stress analyze complicated shapes using real, rather than complex variables, the technique is significant in which it smooths the recorded thermal information, is widely applicable, and requires neither differentiating the measured data nor knowing the elastic properties or external boundary conditions. The latter is extremely important since the external loading is often unknown in practice. That the approach provides the independent stresses is also significant since fatigue analyses and strength criteria typically necessitate knowing the individual components of stress. Present results are supported by those from a finite element analysis, strain gage measurements and load equilibrium.
文摘The perforated stiffened panel is generally found as a sub-component of sophisticated structures.The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental conditions.Hence,an accurate knowledge of critical buckling behaviour of stiffened panels is very much essential for a reliable and lightweight structural design.In this paper,the focus is on quasi-laminated panels with different cutout shapes of various sizes and their responses to hygrothermal environments under nonlinearly varying edge loads and is compared with the locally stiffened panels.Towards this,the modelling of the panel and stiffener is done by adopting nine-noded heterosis plate elements and three noded beam elements respectively.The stiffener formulation is suitably modified in order to take the torsional effect also into consideration along with the effect of shear deformation.Initially,the plate and the stiffener elements are treated separately,and then the displacement compatibility is maintained between them by using the transformation matrix.For a given loading and geometric discontinuity,the stress distribution within the perforated panel is highly non-uniform in nature and hence a dynamic approach has been used to calculate buckling loads by adopting two sets of boundary conditions,one set for pre-buckling stress analysis and the second set for buckling analysis.Four different quasi-isotropic stacking sequences are deliberated in this work by varying different ply-orientation in each scheme.The study also addresses the effect of various parameters such as nonlinear loads,hygro-thermal loads,cutout size and shapes,position of cutout,stiffener parameters,stacking sequences,thickness of plate and boundary conditions.
