A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientat...A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.展开更多
The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relation...The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.展开更多
Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including...Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.展开更多
When the free standing riser(FSR)is in service in the ocean,its mechanical properties are affected by various factors,including complex ocean current forces,buoyancy of the buoyancy can,and torque caused by the deflec...When the free standing riser(FSR)is in service in the ocean,its mechanical properties are affected by various factors,including complex ocean current forces,buoyancy of the buoyancy can,and torque caused by the deflection of the upper floating body.These loads have a great influence on the deformation and internal force of the FSR.The static performance of FSR is investigated in this research under various working conditions.The finite element model of FSR is established based on the co-rotational method.The arc length approach is used to solve the model.The load is exerted in increments.The current load on the riser changes with the configuration of the riser.The accuracy of the numerical method is verified by Abaqus software.The calculation time is also compared.Then,the effects of uniform current,actual current and floating body yaw motion on FSR are studied by parameter analysis.Additionally,the influence of the FSR on the ocean current after the failure of part of the buoyancy can chamber is analyzed.The results show that the numerical model based on the co-rotational method can effectively simulate the large rotation and torsion behavior of FSR.This method has high computational efficiency and precision,and this method can quickly improve the efficiency of numerical calculation of static analysis of deep-water riser.The proposed technology may serve as an alternative to the existing proprietary commercial software,which uses a complex graphical user interface.展开更多
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced....A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.展开更多
A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is intr...A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.展开更多
Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite struc...Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.展开更多
A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper ...A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.展开更多
The planar flexible manipulator undergoing large deformation is investigated by using finite element method (FEM). Three kinds of reference frames are employed to describe the deformation of arbitrary point in the fle...The planar flexible manipulator undergoing large deformation is investigated by using finite element method (FEM). Three kinds of reference frames are employed to describe the deformation of arbitrary point in the flexible manipulator, which are global frame, body-fixed frame and co-rotational frame. The rigid-flexible coupling dynamic equation of the planar flexible manipulator is derived using the Hamilton’s principle. Numerical simulations are carried out in the end of this paper to demonstrate the effectiveness of the proposed model. The simulation results indicate that the proposed model is efficient not only for small deformation but also for large deformation.展开更多
Hard-magnetic soft materials have attracted broad interests because of their flexible programmability,non-contact activation and rapid response in various applications such as soft robotics,biomedical devices and flex...Hard-magnetic soft materials have attracted broad interests because of their flexible programmability,non-contact activation and rapid response in various applications such as soft robotics,biomedical devices and flexible electronics.Such multifunctional materials consist of a soft matrix embedded with hard-magnetic particles,and can exhibit large deformations under external magnetic stimuli.Here,we develop a three-dimensional(3D)rod model to predict spatial deformations(extension,bending and twist)of slender hard-magnetic elastica.The model follows Kirchhoff hypothesis and thus reduces the 3D magneto-elastic energy function to a one-dimensional(1D)form.Besides,the co-rotational formulation is applied to describe rigid body motion,and explicit time integration is adopted for the nonlinear resolution.Moreover,we explore finite bending,post-buckling and twisting of hard-magnetic elastica under external magnetic fields with different directions and amplitudes.Representative examples with various configurations show superior efficiency and accuracy of the model(the difference less than 1%with only a small number of elements)compared to conventional solid element.Our model could be used to guide rational designs on programmable shape morphing of ferromagnetic slender structures.展开更多
In this paper,the co-rotational total Lagrangian forms of finite element formulations are derived to perform elasto-plastic analysis for plane steel frames that either experience increasing external loading at ambient...In this paper,the co-rotational total Lagrangian forms of finite element formulations are derived to perform elasto-plastic analysis for plane steel frames that either experience increasing external loading at ambient temperature or constant external loading at elevated temperatures.Geometric nonlinearities and thermal-expansion effects are considered.A series of programs were developed based on these formulations.To verify the accuracy and efficiency of the nonlinear finite element programs,numerical benchmark tests were performed,and the results from these tests are in a good agreement with the literature.The effects of the nonlinear terms of the stiffness matrices on the computational results were investigated in detail.It was also demonstrated that the influence of geometric nonlinearities on the incremental steps of the finite element analysis for plane steel frames in the presence of fire is limited.展开更多
The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-ro...The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-rotational framework,unified for beam,shell,and brick elements.A unified zero-spin criterion is proposed to specify the local element frame,whose origin is always located at the centroid.Utilizing this criterion,a spin matrix is introduced,and the local frame is invariant to the element nodal ordering.Additionally,the projector matrix is redefined in a more intuitive way,which is the derivative of local co-rotational element frame with respect to the global one.Furthermore,the nodal rotation is obtained with pseudo vector and instantaneous rotation,under a high-order accurate transformation.The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework.Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis.展开更多
基金The project supported by the National Natural Science Foundation of China(19832050 and 10372100)
文摘A constitutive equation theory of Oldroyd fluid B type,i.e.the co-rotational derivative type,is developed for the anisotropic-viscoelastic fluid of liquid crystalline(LC)polymer.Analyzing the influence of the orientational motion on the material behavior and neglecting the influence,the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation,retardation times and anisotropic viscosi- ties are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid.Using the equation for the shear flow of LC polymer fluid,the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al.For the fiber spinning flow of the fluid,the analytical expression of the extensional viscosity is given.
文摘The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.
基金supported,in part,by the National Science Foundation(Grant 1852510).
文摘Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.
基金supported by the National Natural Science Foundation of China(Grant No.52271299).
文摘When the free standing riser(FSR)is in service in the ocean,its mechanical properties are affected by various factors,including complex ocean current forces,buoyancy of the buoyancy can,and torque caused by the deflection of the upper floating body.These loads have a great influence on the deformation and internal force of the FSR.The static performance of FSR is investigated in this research under various working conditions.The finite element model of FSR is established based on the co-rotational method.The arc length approach is used to solve the model.The load is exerted in increments.The current load on the riser changes with the configuration of the riser.The accuracy of the numerical method is verified by Abaqus software.The calculation time is also compared.Then,the effects of uniform current,actual current and floating body yaw motion on FSR are studied by parameter analysis.Additionally,the influence of the FSR on the ocean current after the failure of part of the buoyancy can chamber is analyzed.The results show that the numerical model based on the co-rotational method can effectively simulate the large rotation and torsion behavior of FSR.This method has high computational efficiency and precision,and this method can quickly improve the efficiency of numerical calculation of static analysis of deep-water riser.The proposed technology may serve as an alternative to the existing proprietary commercial software,which uses a complex graphical user interface.
基金the National Natural Science Foundation of China(10372100,19832050)(Key project).
文摘A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid-liquid crystalline （LC） polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie-Ericksen theory is described by the first Rivlin-Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion-extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extru- date of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a seriesof new anisotropic non-Newtonian fluid problems can be addressed.
文摘A new continuum theory of the constitutive equation of co-rotational derivative type is developed for anisotropic viscoelastic fluid—liquid crystalline (LC) polymers. A new concept of simple anisotropic fluid is introduced. On the basis of principles of anisotropic simple fluid, stress behaviour is described by velocity gradient tensor and spin tensor instead of the velocity gradient tensor in the classic Leslie—Ericksen continuum theory. Analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equ- ation of co-rotational type is established for the fluid. A special term of high order in the equation is introduced by author to describe the sp- ecial change of the normal stress differences which is considered as a result of director tumbling by Larson et al. Analyzing the experimental results by Larson et al., a principle of Non- oscillatory normal stress is introduced which leads to simplification of the problem with relaxation times. The special behaviour of non- symmetry of the shear stress is predicted by using the present model for LC polymer liquids. Two shear stresses in shear flow of LC polymer liquids may lead to vortex and rotation flow, i.e. director tumbling in the flow. The first and second normal stress differences are calculated by the model special behaviour of which is in agree- ment with experiments. In the research, the com- putational symbolic manipulation such as computer software Maple is used. For the anisotropic viscoelastic fluid the constitutive equation theory is of important fundamental significance.
基金This work was supported by National Natural Science Foundation of China under Grant 11672266.
文摘Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.
文摘A new continuum theory of the constitutive equation of co-rotational derivative type was developed by the author for anisotropic viscoelastic fluid-liquid crystalline (LC) polymers (S.F. Han, 2008, 2010) . This paper is a continuation of the recent publication [1] to study extrusion-extensional flow of the fluid. A new concept of simple anisotropic fluid is introduced. On the basis of anisotropic simple fluid, stress behavior is described by velocity gradient tensor F and spin tensor W instead of the velocity gradient tensor D in the classic Leslie?Ericksen continuum theory. A special form of the constitutive equation of the co-rotational type is established for the fluid. Using the special form of the constitutive equation in components a computational analytical theory of the extrusion-extensional flow is developed for the LC polymer liquids - anisotropic viscoelastic fluid. Application of the constitutive theory to the flow is successful in predicting bifurcation of elongational viscosity and contraction of extrudate for LC polymer liquids–anisotropic viscoelastic fluid. The contraction of extrudate of LC polymer liquids may be associated with the stored elastic energy conversion into that necessary for bifurcation of elongational viscosity in extrusion extensional flow of the fluid.
基金The National Natural Science Foundation of China(No10372057 No10472065)
文摘The planar flexible manipulator undergoing large deformation is investigated by using finite element method (FEM). Three kinds of reference frames are employed to describe the deformation of arbitrary point in the flexible manipulator, which are global frame, body-fixed frame and co-rotational frame. The rigid-flexible coupling dynamic equation of the planar flexible manipulator is derived using the Hamilton’s principle. Numerical simulations are carried out in the end of this paper to demonstrate the effectiveness of the proposed model. The simulation results indicate that the proposed model is efficient not only for small deformation but also for large deformation.
基金This work was supported by the National Natural Science Foundation of China(Grants Nos.12122204,11872150,and 11890673)Shanghai Pilot Program for Basic Research-Fudan University(Grant No.21TQ1400100-21TQ010)+2 种基金Shanghai Shuguang Program(Grant No.21SG05)Shanghai Rising-Star Program(Grant No.19QA1400500)Young Scientist Project of Ministry of Education Innovation Platform.
文摘Hard-magnetic soft materials have attracted broad interests because of their flexible programmability,non-contact activation and rapid response in various applications such as soft robotics,biomedical devices and flexible electronics.Such multifunctional materials consist of a soft matrix embedded with hard-magnetic particles,and can exhibit large deformations under external magnetic stimuli.Here,we develop a three-dimensional(3D)rod model to predict spatial deformations(extension,bending and twist)of slender hard-magnetic elastica.The model follows Kirchhoff hypothesis and thus reduces the 3D magneto-elastic energy function to a one-dimensional(1D)form.Besides,the co-rotational formulation is applied to describe rigid body motion,and explicit time integration is adopted for the nonlinear resolution.Moreover,we explore finite bending,post-buckling and twisting of hard-magnetic elastica under external magnetic fields with different directions and amplitudes.Representative examples with various configurations show superior efficiency and accuracy of the model(the difference less than 1%with only a small number of elements)compared to conventional solid element.Our model could be used to guide rational designs on programmable shape morphing of ferromagnetic slender structures.
基金This work was sponsored by the National Natural Science Foundation of China(Grant No.10972162).This support is gratefully acknowledged.
文摘In this paper,the co-rotational total Lagrangian forms of finite element formulations are derived to perform elasto-plastic analysis for plane steel frames that either experience increasing external loading at ambient temperature or constant external loading at elevated temperatures.Geometric nonlinearities and thermal-expansion effects are considered.A series of programs were developed based on these formulations.To verify the accuracy and efficiency of the nonlinear finite element programs,numerical benchmark tests were performed,and the results from these tests are in a good agreement with the literature.The effects of the nonlinear terms of the stiffness matrices on the computational results were investigated in detail.It was also demonstrated that the influence of geometric nonlinearities on the incremental steps of the finite element analysis for plane steel frames in the presence of fire is limited.
基金the National Natural Science Foundation of China(Grant Nos.11972297 and 11972300)the Fundamental Research Funds for the Central Universities of China(Grant No.G2019KY05203).
文摘The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-rotational framework,unified for beam,shell,and brick elements.A unified zero-spin criterion is proposed to specify the local element frame,whose origin is always located at the centroid.Utilizing this criterion,a spin matrix is introduced,and the local frame is invariant to the element nodal ordering.Additionally,the projector matrix is redefined in a more intuitive way,which is the derivative of local co-rotational element frame with respect to the global one.Furthermore,the nodal rotation is obtained with pseudo vector and instantaneous rotation,under a high-order accurate transformation.The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework.Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis.
