Research On The Non-Linear And Stability Analysis Of Large Flexible Structure Based On The Absolute Nodal Coordinate Formulation

Absolute Nodal Coordinate Formulation(ANCF)is a finite element method using kinematic description in the absolute coordinate system.Position and position gradient vectors are directly used as the degree of freedom of nodes,and there are no restrictions on the deformation and rotation of elements.Therefore,the absolute nodal coordinate formulation is particularly suitable for problems with large deformation and large rotation characteristics.Due to the merit of constant mass matrix,the absolute nodal coordinate formulation was first applied to the flexible multi-body dynamics analysis.At the same time,because the description of strain and stress is consistent with general continuum mechanics,the absolute nodal coordinate formulation was gradually applied to the nonlinear statics analysis.For the typical nonlinear problem,buckling and postbuckling of structures,the absolute node coordinate formulation is rarely used.Under the framework of absolute nodal coordinate formulation,this thesis explores the application procedure of ANCF method,and demonstrates the potential of the ANCF method in nonlinear structural buckling analysis via modifying the numerical procedure for nonlinear buckling and postbuckling analysis and analysis of beam-column,arch,and frame structures.This thesis tries to fill in the deficiency of absolute node-coordinate method in nonlinear buckling analysis,enrich its connotation as a comprehensive nonlinear finite element method,and provide a new direction for nonlinear analysis of complex structures.Lateral perturbation method was used to analyze the out-of-plane buckling of column and the cable-beam structure.Four different types of ANCF beam element,i.e.,the original beam element(Om Sh)based on standard continuum mechanics,element modified by the strain split method(SSM),the higher order beam element(HOBE),and element improved by the enhanced continuum mechanics(En CM)method were studied.The Om Sh element suffers locking problem due to low interpolation in the transverse direction.The influence of locking on stability analysis was presented.It was proved by the out-of-plane buckling of the cable-beam structure with the beam guyed by cable that the ANCF higher order element exhibits high accuracy in the structural stability analysis(bifurcation instability).Then,the numerical procedure of postbuckling analysis based on the absolute nodal coordinate formulation was constructed.Three ANCF planar beam elements,i.e.,Om Sh element,SSM element,and HOBE element,were used to conduct nonlinear postbuckling analysis of the arch structure,and trace its postbuckling trajectory.Circular arches with different geometric configurations and boundary conditions were analyzed,including fixed-fixed,hinged-hinged,fixed-hinged,and three-hinged arch structures.The structures showed nonlinear responses of snap-through,snap-back,and looping phenomenon.The results obtained are in good agreement with the analytical solution,the experimental results in the literature,and the commercial finite element software.The feasibility of absolute nodal coordinate formulation in the postbuckling analysis was verified,and the merits and demerits of three ANCF beam elements in the applicability of arc-length method were presented.For the structure with slope discontinuity,a structural coordinate system was introduced to solve the problem of slope discontinuity in modeling structures such as Lee’s frame.The nonlinear postbuckling analysis of Lee’s frame subjected to concentrated force was carried out by using four ANCF planar beam elements,i.e.,Om Sh element,SSM element,En CM element,and HOBE element.Two buckling load estimation methods were used,i.e.,tracking the nonlinear equilibrium path of the load-displacement space by using the arc length method,and tracking the energy criterion of the eigenvalues by using the dichotomy method.Lee’s frames with different boundary conditions were studied.The complicated nonlinear responses such as snap-through,snap-back,and looping phenomenon of Lee’s frame were simulated.The critical buckling load and buckling mode shapes were obtained by buckling method based on energy criterion.The limit point of the buckling load and critical buckling load obtained by the two methods were compared,and the performance of four different elements was compared.In addition to geometric nonlinearity,the application of absolute nodal coordinate formulation in the material nonlinearity was further explored,such as the large deformation,postbuckling,and stability analysis of axially functionally graded beam structures.The stability of axially functionally graded material(AFGM)cantilever beam was analyzed by Om Sh element,En CM element,and HOBE element.The material distribution along the longitudinal axis of AFGM beam was described by power law distribution,and the constitutive materials were steel and aluminum.The large deformation analysis of AFGM beam was carried out by using full Newton-Raphson iteration method.The Crisfield arc-length method was used to simulate the nonlinear postbuckling response.The dichotomy method based scheme to estimate the critical buckling load was used.The results are in agreement with the existing literature,demonstrating the effectiveness of ANCF method in nonlinear buckling analysis of AFGM beam.