Generalized mixed finite element method for 3D elasticity problems

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.

A Generalized Point Conforming Rectangular Plate Element

A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).

ON THE EQUIVALENCE OF THE WILSON ELEMENT AND THE GENERALIZED HYBRID ELEMENT

In this paper the equivalence of the generalized hybrid element and the modified Wilson element, which is derived by the generalized hybrid method, is proved.

A hybrid finite volume/finite element method for incompressible generalized Newtonian fluid flows on unstructured triangular meshes

This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.

A RECTANGULAR ELEMENT OF THIN PLATES BASED UPON THE GENERALIZED VARIATIONAL PRINCIPLES

Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.

Design of a d_(33)-mode piezocomposite electricity generating element and its application to bridge monitoring

The piezoelectric effect is used in sensing applications such as in force and displacement sensors.However,the brittleness and low performance of piezoceramic lead zirconate titanate(PZT) often impede its applicability in civil structures which are subjected to large loads.The concept of a piezocomposite electricity generating element(PCGE) has been proposed for improving the electricity generation performance and overcoming the brittleness of piezoceramic wafers.The post-curing residual stress in the PZT layer constitutes a main reason for the PCGE's enhanced performance,and the outer epoxy-based composites protect the brittle PZT layer.A d33-mode PCGE designed for bridge monitoring application was inserted in a bridge bearing to provide a permanent and simple weigh-in-motion system.The designed PCGEs were tested through a series of tests including fatigue and dynamic tests to verify their applicability for monitoring purposes in a bridge structure.A simple beam example was presented to show the applicability of the proposed bridge bearing equipped with the PCGE for adequately measuring the traffic loads.

ON THE SPECTRAL EQUIVALENCE OF UNCONVENTIONAL FINITE ELEMENTS AND THEIR CONVENTIONAL RELATIVES

With a generalized conforming element as a typical example, the spectral equivalence of unconventional finite elements and their conventional relatives is proved. This result is very important for the construction of domain decomposition parallel algorithms for unconventional finite elements.

Generalized Multiscale Finite Element Methods.Nonlinear Elliptic Equations

In this paper we use the Generalized Multiscale Finite Element Method(GMsFEM)framework,introduced in[26],in order to solve nonlinear elliptic equations with high-contrast coefficients.The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation.With this convention,we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin(CG)or discontinuous Galerkin(DG)global formulations.Here,we use Symmetric Interior Penalty Discontinuous Galerkin approach.Both methods yield a predictable error decline that depends on the respective coarse space dimension,and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples.

A Simplified Approach to Analysis of High-Rise Frame Tube Structures

Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.

The Existence of the Complete and Completely Distributive Lattices

The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory. In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the in flute complete and completely distributive lattice which has finite dimension.A complete boolean lattice B possesses the smallest set of generating elements iff B is completely distributive.

On the Smallest Base of the Stone Space

In this paper,first we define the concept of strong open set for topological space. Then we prove: 1 ) a distributive lattice L possesses the smallest set of generating elements if and only if the Stone space (L) of L possesses a smallest base constructed by strong open sets; 2) a Bollean lattice B possesses the smallest set of generating elements if and only if B is a finite Boolean lattice.

Time-Lapse 3-D Seismic Wave Simulation via the Generalized Multiscale Finite Element Method

Numerical solution of time-lapse seismic monitoring problems can be challenging due to the presence of finely layered reservoirs.Repetitive wave modeling using fine layered meshes also adds more computational cost.Conventional approaches such as finite difference and finite element methods may be prohibitively expensive if the whole domain is discretized with the cells corresponding to the grid in the reservoir subdomain.A common approach in this case is to use homogenization techniques to upscale properties of subsurface media and assign the background properties to coarser grid;however,inappropriate application of upscaling might result in a distortion of the model,which hinders accurate monitoring of the fluid change in subsurface.In this work,we instead investigate capabilities of a multiscale method that can deal with fine scale heterogeneities of the reservoir layer and more coarsely meshed rock properties in the surrounding domains in the same fashion.To address the 3-D wave problems,we also demonstrate how the multiscale wave modeling technique can detect the changes caused by fluid movement while the hydrocarbon production activity proceeds.

Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems

In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems.It is based on the generalized multiscale finite element method(GMsFEM)and multilevel Monte Carlo(MLMC)methods.The former provides a hierarchy of approximations of different resolution,whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels.The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost,and to efficiently generate samples at different levels.In particular,it is cheap to generate samples on coarse grids but with low resolution,and it is expensive to generate samples on fine grids with high accuracy.By suitably choosing the number of samples at different levels,one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces,while retaining the accuracy of the final Monte Carlo estimate.Further,we describe a multilevel Markov chain Monte Carlo method,which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids,while combining the samples at different levels to arrive at an accurate estimate.The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in[26],and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates.