A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations

A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.

Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation

The simulation of Rayleigh waves is important in a variety of geophysical applications.The computational challenge is the fact that very fine mesh is necessary as the waves are concentrated at the free surface and decay exponentially away from the free surface.To overcome this challenge and to develop a robust high order scheme for the simulation of Rayleigh waves,we develop a mortar discontinuous Galerkin method with staggered hybridization.The use of the mortar technique allows one to use fine mesh in only a local region near the free surface,and use coarse mesh in most of the domain.This approach reduces the computational cost significantly.The staggered hybridization allows the preservation of the strong symmetry of the stress tensor without complicated construction of basis functions.In particular,the basis functions are piecewise polynomial without any continuity requirement,and the coupling of the basis functions is performed by using carefully chosen hybridized variables.The resulting scheme is explicit in time,and only local saddle point system are solved for each time step.We will present several benchmark problems to demonstrate the performance of the proposed method.

正则和奇异自共轭微分算子的变分公式化(英文)

A variational formulation for regular and singular symmetric second order differen- tial operators is obtained under very general conditions on the data of the problem. The variational form obtained is equivalent to the general self-adjoint realization of the differential operator. Two new properties of certain operators associated with the problem are also discovered.