Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into seve...Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into several wave bands so as to be effectively absorbed by photovoltaic materials with different band gaps. A new method is proposed for designing high-efficiency SSBC DOEs, which is physically simple, numerically fast, and universally applicable. The SSBC DOEs are designed by the new design method, and their performances are analyzed by the Fresnel diffraction integral method.The new design method takes two advantages over the previous design method. Firstly, the optical focusing efficiency is heightened by up to 10%. Secondly, focal positions of all the designed wavelengths can be designated arbitrarily and independently. It is believed that the designed SSBC DOEs should have practical applications to solar cell systems.展开更多
The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were der...The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.展开更多
Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation th...Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.展开更多
The matrix eigenvalue method is used to analyze a laser resonator composed of diffraction optical elements. The results show that this type of resonator can separate fundamental mode and high order modes effectively. ...The matrix eigenvalue method is used to analyze a laser resonator composed of diffraction optical elements. The results show that this type of resonator can separate fundamental mode and high order modes effectively. The output beams can be designed for different requests.展开更多
Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Eul...Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.展开更多
To meet the demand for an accurate and highly efficient damage model with a distinct physical meaning for performance-based earthquake engineering applications, a stiffness degradation-based damage model for reinforce...To meet the demand for an accurate and highly efficient damage model with a distinct physical meaning for performance-based earthquake engineering applications, a stiffness degradation-based damage model for reinforced concrete （RC） members and structures was developed using fiber beam-column elements. In this model, damage indices for concrete and steel fibers were defined by the degradation of the initial reloading modulus and the low-cycle fatigue law. Then, section, member, story and structure damage was evaluated by the degradation of the sectional bending stiffness, rod-end bending stiffness, story lateral stiffness and structure lateral stiffness, respectively. The damage model was realized in Matlab by reading in the outputs of OpenSees. The application of the damage model to RC columns and a RC frame indicates that the damage model is capable of accurately predicting the magnitude, position, and evolutionary process of damage, and estimating stow damage more precisely than inter-story drift. Additionally, the damage model establishes a close connection between damage indices at various levels without introducing weighting coefficients or force-displacement relationships. The development of the model has perfected the damage assessment function of OpenSees, laying a solid foundation for damage estimation at various levels of a large-scale structure subjected to seismic loading.展开更多
A design approach for optical interconnect system and beam splitting composed of a phase-only diffractive optical element is described.The diffractive optical element is of 16 phase levels,so its efficiency may reach ...A design approach for optical interconnect system and beam splitting composed of a phase-only diffractive optical element is described.The diffractive optical element is of 16 phase levels,so its efficiency may reach very high.Three examples of interconnect and beam splitting patterns are carried out with this design approach and the satisfactory results are given.展开更多
In the Fresnel transform domain, an effective improvement to the conventional iterative algorithm for designing the diffractive optical elements (DOEs) used for spatial beam shaping has been proposed. The algorithm ca...In the Fresnel transform domain, an effective improvement to the conventional iterative algorithm for designing the diffractive optical elements (DOEs) used for spatial beam shaping has been proposed. The algorithm can successfully achieve to design DOEs for beam shaping. Compared with conventional algorithm, this algorithm can provide faster convergence, more powerful ability to overcome local minimum problem and better shaping quality. By computer simulation, the result has shown that the DOEs designed by this algorithm has snch advantages as high uniformity at the main lobe, low profile error and steep edge.展开更多
This paper investigates the free vibration and transient response of interconnected structures including double curved beams and intermediate straight beams,which are all constructed from functionally graded porous(FG...This paper investigates the free vibration and transient response of interconnected structures including double curved beams and intermediate straight beams,which are all constructed from functionally graded porous(FGP)materials.The strain potential and kinetic energies of each beam along with the work done by the external force are calculated.Additionally,a higher-order beam element is introduced to derive stiffness and mass matrices,along with the force vector.The curved and straight beams are discretized,and their assembled stiffness,mass matrices,and force vectors,are obtained.Continuity conditions at the joints are used to derive the total matrices of the entire structure.Subsequently,the natural frequencies and transient response of the system are determined.The accuracy of the mathematical model and the self-developed computer program is validated through the comparison of the obtained results with those of the existing literature and commercial software ANSYS,demonstrating excellent agreement.Furthermore,a comprehensive study is conducted to investigate the effects of various parameters on the free vibration and transient response of the considered structure.展开更多
The finite segment modelling for the flexible beam-formed structural elements is presented, in which the discretization views of the finite segment method and the difference from the finite element method are introduc...The finite segment modelling for the flexible beam-formed structural elements is presented, in which the discretization views of the finite segment method and the difference from the finite element method are introduced. In terms of the nodal model, the joint properties are described easily by the model of the finite segment method, and according to the element properties, the assumption of the small strain is only met in the finite segment method, i. e., the geometric nonlinear deformation of the flexible bodies is allowable. Consequently,the finite segment method is very suited to the flexible multibody structure. The finite segment model is used and the are differentiation is adopted for the differential beam segments. The stiffness equation is derived by the use of the principle of virtual work. The new modelling method shows its normalization, clear physical and geometric meanings and simple computational process.展开更多
Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such a...Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.展开更多
This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-...This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.展开更多
A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical a...A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.展开更多
Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent ...Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in total Lagarange(TL) and the corresponding stiffness matrix are formulated.Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss.Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method.Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.展开更多
An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal p...An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.展开更多
A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces...A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.展开更多
Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the...Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.展开更多
A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved usi...A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.展开更多
Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient ...Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.展开更多
基金Project supported by the National Basic Research Program of China(Grant No.2013CBA01702)the National Natural Science Foundation of China(Grant Nos.11474206,91233202,11374216,and 11404224)+1 种基金the Scientific Research Project of Beijing Education Commission,China(Grant No.KM201310028005)the Scientific Research Base Development Program of the Beijing Municipal Commission of Education and the Beijing Youth Top-Notch Talent Training Plan,China(Grant No.CIT&TCD201504080)
文摘Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into several wave bands so as to be effectively absorbed by photovoltaic materials with different band gaps. A new method is proposed for designing high-efficiency SSBC DOEs, which is physically simple, numerically fast, and universally applicable. The SSBC DOEs are designed by the new design method, and their performances are analyzed by the Fresnel diffraction integral method.The new design method takes two advantages over the previous design method. Firstly, the optical focusing efficiency is heightened by up to 10%. Secondly, focal positions of all the designed wavelengths can be designated arbitrarily and independently. It is believed that the designed SSBC DOEs should have practical applications to solar cell systems.
文摘The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.
基金the National Natural Science Foundation of China(No.10472102)theNational Basic Research Program of China(No.2007CB714200)
文摘Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.
基金This project is supported by the National Natural Science Foundation of China under the Grant No. 19970438.
文摘The matrix eigenvalue method is used to analyze a laser resonator composed of diffraction optical elements. The results show that this type of resonator can separate fundamental mode and high order modes effectively. The output beams can be designed for different requests.
文摘Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.
基金the National Natural Science Foundation of China under Grant Nos.51278218 and 51078166
文摘To meet the demand for an accurate and highly efficient damage model with a distinct physical meaning for performance-based earthquake engineering applications, a stiffness degradation-based damage model for reinforced concrete （RC） members and structures was developed using fiber beam-column elements. In this model, damage indices for concrete and steel fibers were defined by the degradation of the initial reloading modulus and the low-cycle fatigue law. Then, section, member, story and structure damage was evaluated by the degradation of the sectional bending stiffness, rod-end bending stiffness, story lateral stiffness and structure lateral stiffness, respectively. The damage model was realized in Matlab by reading in the outputs of OpenSees. The application of the damage model to RC columns and a RC frame indicates that the damage model is capable of accurately predicting the magnitude, position, and evolutionary process of damage, and estimating stow damage more precisely than inter-story drift. Additionally, the damage model establishes a close connection between damage indices at various levels without introducing weighting coefficients or force-displacement relationships. The development of the model has perfected the damage assessment function of OpenSees, laying a solid foundation for damage estimation at various levels of a large-scale structure subjected to seismic loading.
文摘A design approach for optical interconnect system and beam splitting composed of a phase-only diffractive optical element is described.The diffractive optical element is of 16 phase levels,so its efficiency may reach very high.Three examples of interconnect and beam splitting patterns are carried out with this design approach and the satisfactory results are given.
文摘In the Fresnel transform domain, an effective improvement to the conventional iterative algorithm for designing the diffractive optical elements (DOEs) used for spatial beam shaping has been proposed. The algorithm can successfully achieve to design DOEs for beam shaping. Compared with conventional algorithm, this algorithm can provide faster convergence, more powerful ability to overcome local minimum problem and better shaping quality. By computer simulation, the result has shown that the DOEs designed by this algorithm has snch advantages as high uniformity at the main lobe, low profile error and steep edge.
文摘This paper investigates the free vibration and transient response of interconnected structures including double curved beams and intermediate straight beams,which are all constructed from functionally graded porous(FGP)materials.The strain potential and kinetic energies of each beam along with the work done by the external force are calculated.Additionally,a higher-order beam element is introduced to derive stiffness and mass matrices,along with the force vector.The curved and straight beams are discretized,and their assembled stiffness,mass matrices,and force vectors,are obtained.Continuity conditions at the joints are used to derive the total matrices of the entire structure.Subsequently,the natural frequencies and transient response of the system are determined.The accuracy of the mathematical model and the self-developed computer program is validated through the comparison of the obtained results with those of the existing literature and commercial software ANSYS,demonstrating excellent agreement.Furthermore,a comprehensive study is conducted to investigate the effects of various parameters on the free vibration and transient response of the considered structure.
基金National Natural Science Foundation of China!59575026
文摘The finite segment modelling for the flexible beam-formed structural elements is presented, in which the discretization views of the finite segment method and the difference from the finite element method are introduced. In terms of the nodal model, the joint properties are described easily by the model of the finite segment method, and according to the element properties, the assumption of the small strain is only met in the finite segment method, i. e., the geometric nonlinear deformation of the flexible bodies is allowable. Consequently,the finite segment method is very suited to the flexible multibody structure. The finite segment model is used and the are differentiation is adopted for the differential beam segments. The stiffness equation is derived by the use of the principle of virtual work. The new modelling method shows its normalization, clear physical and geometric meanings and simple computational process.
基金supported by the National Science Fund for Distinguished Young Scholars (No. 50725826).
文摘Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.
基金supported by the National Natural Science Foundation of China (No.50935008)
文摘This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.
文摘A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.
基金supported by the National Natural Science Foundation of China(Grant No.50725826)
文摘Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in total Lagarange(TL) and the corresponding stiffness matrix are formulated.Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss.Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method.Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.
基金the National Natural Science Foundation of China (Grants 11521062, 11722216)the 111 China Project (Grant B16003)+1 种基金Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant KYCX17_0226)China Scholarship Council.
文摘An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.
基金The project supported by the National Natural Science Foundation of China(10172023)
文摘A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.
基金supported by the National Natural Science Foundation of China(10872126)Research Fund for the Doctoral Program of Higher Education of China(20100073110007)
文摘Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.
基金National Program on Key Basic Research Project of China (973) under Grant No.2011CB013603National Natural Science Foundation of China under Grant Nos.51008208,51378341+1 种基金Projects International Cooperation and Exchanges NSFC (NSFC-JST) under Grant No.51021140003Tianjin Municipal Natural Science Foundation under Grant No.13JCQNJC07200
文摘A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.
基金The project was financially supported by the National Natural Science Foundation of China
文摘Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.
