Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decom...Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decomposed into a series of matrices with respect to the assumed strain modes. The formulation presented in this paper is different from any other non linear mixed/hybrid element formulation all successful experience of linear hybrid formulation is absorbed into the formulation(adding non conforming modes and realizing orthogonalization) Numerical results show that the present approach is more effective than any other non linear hybrid element formulation over the accuracy and computational efficiency. In addition, non conforming modes can also overcome the shear locking effect.展开更多
An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acousti...An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.展开更多
The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinea...The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching, the influence of volume fraction profile parameter and temperature change. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Taking the temperature-dependency of the effective material properties into consideration, the Voigt model is used to simulate the material properties of the FGMs （functionally graded materials）. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using DQM （differential quadrature method）. The natural frequencies of clamped-clamped micro-switches are obtained. The solutions are validated through direct comparisons with experimental results reported in previous studies. A parametric study is conducted to show the effects of geometric nonlinearity, material composition, temperature change and geometrical parameters for the natural frequencies.展开更多
The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to e...The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to each other, and any change in thickness will result in change in stiffness in any direction. In latticed shells, members are discrete and stiffnesses in two mutually perpendicular directions are discontinuous and independent of each other. Therefore, sensitivity of geometrical imperfection for buckling of latticed shells should be different from that of continuum shells. The author proposes a shape optimization method for maximum buckling load of a latticed shell. A single layer latticed dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that of its initial shape. Furthermore, the numerical example demonstrates that an optimum latticed shell with maximum buckling load, unlike an optimum continuum shell, may not be sensitive to its geometrical imperfection.展开更多
A linearization method and an engineering approach for the geometric nonlinear aeroelastic stability analysis of the very flexi- ble aircraft with high-aspect-ratio wings are established based on the little dynamic pe...A linearization method and an engineering approach for the geometric nonlinear aeroelastic stability analysis of the very flexi- ble aircraft with high-aspect-ratio wings are established based on the little dynamic perturbation assumption.The engineering practicability of the method is validated by a complex example.For a high-altitude long-endurance unmanned aircraft,the nonlinear static deformations under straight flight and the gust loads are calculated.At the corresponding nonlinear equilibrium state,the complete aircraft is linearized dynamically and the vibration modes are calculated considering the large deformation effects.Then the unsteady aerodynamics are calculated by the double lattice method.Finally,the aeroelastic stability of the complete aircraft is analyzed.The results are compared with the traditional linear calculation.The work shows that the geometric nonlinearity induced by the large structural deformation leads to the motion coupling of the wing chordwise bending and the torsion,which changes the mode frequencies and mode shapes.This factors change the aeroelastic coupling relationship of the flexible modes leading to the decrease of the flutter speed.The traditional linear method would give not only an imprecise flutter speed but also a possible dramatic mistake on the stability.Hence,for a high-altitude long-endurance unmanned aircraft with high-aspect-ratio wings,or a similar very flexible aircraft,the geometric nonlinear aeroelastic analysis should be a necessary job in engineering practice.展开更多
文摘Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decomposed into a series of matrices with respect to the assumed strain modes. The formulation presented in this paper is different from any other non linear mixed/hybrid element formulation all successful experience of linear hybrid formulation is absorbed into the formulation(adding non conforming modes and realizing orthogonalization) Numerical results show that the present approach is more effective than any other non linear hybrid element formulation over the accuracy and computational efficiency. In addition, non conforming modes can also overcome the shear locking effect.
基金supported by the National Natural Science Foundations of China(Nos.11872079,11572109)the Science and Technology Project of Hebei Education Department(No.QN2019135)Advanced Talents Incubation Program of the Hebei University(No.521000981285)。
文摘An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.
基金Acknowledgments The research was financially supported by the National Natural Science Foundation of China （Grant No. 11402309） and the Science Foundation of China University of Petroleum, Beijing （No. YJRC-2013-32）.
文摘The free vibration characteristics of functionally graded micro-switches under combined electrostatic, axial residual stress and temperature change is investigated, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching, the influence of volume fraction profile parameter and temperature change. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Taking the temperature-dependency of the effective material properties into consideration, the Voigt model is used to simulate the material properties of the FGMs （functionally graded materials）. The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using DQM （differential quadrature method）. The natural frequencies of clamped-clamped micro-switches are obtained. The solutions are validated through direct comparisons with experimental results reported in previous studies. A parametric study is conducted to show the effects of geometric nonlinearity, material composition, temperature change and geometrical parameters for the natural frequencies.
文摘The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to each other, and any change in thickness will result in change in stiffness in any direction. In latticed shells, members are discrete and stiffnesses in two mutually perpendicular directions are discontinuous and independent of each other. Therefore, sensitivity of geometrical imperfection for buckling of latticed shells should be different from that of continuum shells. The author proposes a shape optimization method for maximum buckling load of a latticed shell. A single layer latticed dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that of its initial shape. Furthermore, the numerical example demonstrates that an optimum latticed shell with maximum buckling load, unlike an optimum continuum shell, may not be sensitive to its geometrical imperfection.
基金supported by the National Natural Science Foundation of China(Grant Nos.90716006,10902006)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20091102110015)
文摘A linearization method and an engineering approach for the geometric nonlinear aeroelastic stability analysis of the very flexi- ble aircraft with high-aspect-ratio wings are established based on the little dynamic perturbation assumption.The engineering practicability of the method is validated by a complex example.For a high-altitude long-endurance unmanned aircraft,the nonlinear static deformations under straight flight and the gust loads are calculated.At the corresponding nonlinear equilibrium state,the complete aircraft is linearized dynamically and the vibration modes are calculated considering the large deformation effects.Then the unsteady aerodynamics are calculated by the double lattice method.Finally,the aeroelastic stability of the complete aircraft is analyzed.The results are compared with the traditional linear calculation.The work shows that the geometric nonlinearity induced by the large structural deformation leads to the motion coupling of the wing chordwise bending and the torsion,which changes the mode frequencies and mode shapes.This factors change the aeroelastic coupling relationship of the flexible modes leading to the decrease of the flutter speed.The traditional linear method would give not only an imprecise flutter speed but also a possible dramatic mistake on the stability.Hence,for a high-altitude long-endurance unmanned aircraft with high-aspect-ratio wings,or a similar very flexible aircraft,the geometric nonlinear aeroelastic analysis should be a necessary job in engineering practice.
