The generalized finite element method (GFEM) is versatile and powerful in the numerical analysis of various engineering problems. However, its application to large deformation analysis of elastoplastic solids is rare, especially in three dimensions (3D), since it suffers from singular system matrix and awkward implementation. This issue is caused by the extra degrees of freedom (DOFs) of GFEM. In this work, a nonlinear GFEM for large deformation analysis of elastic and elastoplastic solids in 3D is developed by using the extra-DOF-free enrichments proposed by Tian (2013) Updated Lagrangian (UL) formulation incorporating both geometric and material nonlinearities is employed and hyperelastic and hypoelastic–plastic constitutive models are considered. As a result of the elimination of the extra DOFs, implementation of the developed method is much more convenient than the standard GFEM and singular system matrix does not present. The capability of the proposed nonlinear GFEM in modeling three-dimensional large elastoplastic deformations is investigated by several typical examples. Numerical results demonstrate that, in comparison to the traditional finite element method, the proposed nonlinear GFEM is remarkably more accurate and stable. Particularly, in analysis of extreme deformations, the commercial software ABAQUS fails even when sophisticated elements are used, however the proposed nonlinear extra-DOF-free GFEM is still stable and converged results can be obtained.
This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.
In order to solve the problems of the classical fifth-order weighted essentially non-oscillatory(WENO)scheme,such as the excessive dissipation near the discontinuity and the inaccurate preserving of the critical point,a new modified stencil approximation method is proposed.The second-order polynomial approximation of the numerical flux on each candidate sub-stencil in the classical fifth-order WENO-JS scheme is improved,and the stencil approximation reaches the fourth-order accuracy by adding a cubic correction term.The new scheme has ENO property by introducing adjustable function φ,and the theoretical analysis shows that the new scheme has accuracy-preserving property.A series of numerical examples show the efficiency of the new scheme.
In order to analyze the distortion effect of trapezoidal composite box girder with corrugated steel webs and steel bottom plates,the restraint effect of top and bottom plates on corrugated steel webs is considered.Maintain the in-plane and out-of-plane bending stiffness unchanged when the composite box girder is equivalent to a steel box girder.Based on the plate element frame method,the distortion governing differential equation is set up based on plate element frame method and the general solution of Krylov function is derived.Combined with the comparative analysis of numerical examples,the rationality of this method is verified,and the influence of web depression angle and girder height on bi-moments is studied.The results demonstrate that it is more reasonable to consider the restraint effect of the top and bottom plates on the webs than to ignore the in-plane bending stiffness of the webs completely.As distortion warping stiffness and transverse frame stiffness of box girder is greatly weakened by corrugated steel web and steel bottom plate,the distortion warping stress of traditional corrugated steel web composite box girder can reach 1.98 times that of ordinary concrete box girder.And the distortion warping stress of corrugated steel web composite box girder with steel bottom plate can reach 15.31 times of that of traditional corrugated steel web composite box girder.The bi-moment near the mid-span section changes little with the web depression angle,and the bi-moment in other sections decreases gradually with the increase of the web depression angle.The distortion bi-moment increases slightly with the increase of girder height,and its maximum position changes.
In order to study the distortion effect of a composite concrete box girder with a steel truss web,on the basis of the thin-walled box girder theory,considering the mechanical properties of the steel truss web,the improved plate element analytic method is used to establish the differential equation for distortion.The distortion analytical solution are given.A solid model through ANSYS to verify the correctness of the derived formula is established.Combined with numerical examples,the distortion stresses of a composite box girder and a traditional concrete box girder with the same cross-sectional parameters under a uniformly distributed distortion load are compared and analyzed.The influence of the beam width and the depression angle of the steel web on the distortion internal force of the composite box girder is analysed.The results show that under the same section parameters,due to the small longitudinal stiffness of the steel truss web member of the composite box girder,of which distortion warping normal stress is 1.71 times of that of the concrete box girder;the beam width has a great influence on the distortion internal force,and when the beam width increases to 4.5 m,the distortion double moment and the distortion moment increase to 3.68 times and 1.36 times respectively,and the distribution trend of the former two peaks in the longitudinal direction is gradually flat;When the depression angle of the steel web increases to 27°,the distortion double moment is reduced by about 14.3％,but it has little effect on the distortion moment.
