A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

A REDUCED MFE FORMULATION BASED ON POD FOR THE NON-STATIONARY CONDUCTION-CONVECTION PROBLEMS

In this article, a reduced mixed finite element （MFE） formulation based on proper orthogonal decomposition （POD） for the non-stationary conduction-convection problems is presented. Also the error estimates between the reduced MFE solutions based on POD and usual MFE solutions are derived. It is shown by numerical examples that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced MFE formulation based on POD is feasible and efficient in finding numerical solutions for the non-stationary conduction-convection problems.

THEORETICAL BASIS AND GENERAL OPTIMAL FORMULATIONS OF ISOPARAMETRIC GENERALIZED HYBRID/MIXED ELEMENT MODEL FOR IMPROVED STRESS ANALYSIS

By the modified three-field Hu-Washizu principle, this paper establishes a theoretical founda- tion and general convenient formulations to generate convergent stable generalized hybrid/mixed cle- ment (GH/ME) model which is invariant with respect to coordinate, insensitive to geometric distortion and suitable for improved stress computation. In the two proposed formulations, the stress equilibrium and orthogonality constraints are imposed through incompatible displacement and internal strain modes respectively. The proposed model by the general formulations in this paper is characterized by including as- sumed stress/strain, assumed stress, variable-node, singular, compatible and incompatible GH/ME models. When using regular meshes or the constant values of the isoparametric Jacobian Det in the assumed strain in- terpolation, the incompatible GH/ME model degenerates to the hybrid/mixed element model. Both general and concrete guidelines for the optimal selection of element shape functions are suggested. By means of the GH/ME theory in this paper, a family of new GH/ME can be and have been easily constructed. The software can also be developed conveniently because all the standard subroutines for the corresponding isoparametric displacement elements can be utilized directly.

A REDUCED FE FORMULATION BASED ON POD METHOD FOR HYPERBOLIC EQUATIONS

A proper orthogonal decomposition（POD） method was successfully used in the reduced-order modeling of complex systems.In this paper,we extend the applications of POD method,namely,apply POD method to a classical finite element（FE） formulation for second-order hyperbolic equations with real practical applied background,establish a reduced FE formulation with lower dimensions and high enough accuracy,and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications.Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions.Moreover,it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.

A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS

A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.

A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS

In this article, a proper orthogonal decomposition （POD） method is used to study a classical splitting positive definite mixed finite element （SPDMFE） formulation for second- order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations.

Variation principle of piezothermoelastic bodies,canonical equation and homogeneous equation

Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.

A FINITE ELEMENT ANALYSIS OF THE LARGE PLASTIC DEFORMATION BEHAVIOR OF AMORPHOUS GLASSY CIRCULAR POLYMERIC BARS

The BPA eight-chain molecular network model is introduced into the finite element formulation of elastic-plastic large deformation. And then, the tensile deformation localization development of the amorphous glassy circular polymeric bars (such as polycarbonates) is numerically simulated. The simulated results are compared with experimental ones, and very good consistence between numerical simulation and experiment is obtained, which shows the efficiency of the finite element analysis. Finally, the influences of the microstructure parameter S-ss on tensile neck-propagation and triaxial stress effect are studied.

Finite element formulation based on proper orthogonal decomposition for parabolic equations

A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.

Mass Flow Prediction of the Coriolis Meter using C^0 Continuous Beam Elements

A three node C^0 continuous isoparametric beam element is formulated to model the curved pipe conveying fluid in three dimensional configuration.The equations of motion for the combined structure and fluid domain including added mass effect,Coriolis effect,centrifugal effect and the effect of pressure on the walls of pipe have been developed by Paidoussis.This equation is converted to finite element formulation using Galerkin technique and is validated with the results available from literature.

Nonlinear Bifurcation and Post-buckling Analysis of Cylindrical Composite Stiffened Laminates Based on Weak Form Quadrature Element Method

This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian updating scheme is used in combination with arc-length method,and the branch-switching method is adopted to identify the whole post-buckling procedure of the laminates.The formulation of the shell model and beam model are based on the basic concept of Ahmad.The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of the cylindrical stiffened laminates.Several numerical examples are firstly presented to verify the effectiveness and accuracy of present formulation.Parametric studies on the effects of the height-to-breadth ratio,lamination schemes,positions,distribution,number of the stiffeners on the bifurcation and post-buckling behavior are performed.

Hypoplastic particle finite element model for cutting tool-soil interaction simulations:Numerical analysis and experimental validation

This study presents numerical and experimental models for the analysis of the excavation of soft soils by means of a cutting tool.The computational model is constructed using an Updated Lagrangean(UL)velocity-based Finite Element approach.A hypoplastic formu-lation is employed to describe the constitutive behavior of soft soils.Large displacements and deformations of the ground resulting from the cutting tool-soil interaction are handled by means of the Particle Finite Element method,characterized by a global re-meshing strat-egy and a boundary identification procedure called a-shape technique.The capabilities and performance of the proposed model are demonstrated through comparative analyses between experiments and simulations of cutting tool-soft soil interactions.The experiments are performed using an excavation device at Ruhr-Universita¨t Bochum(RUB),Germany.The main details concerning the setup and calibration and evolution of the measured draft forces are discussed.Selected computational results characterizing the cutting tool-soft soil interaction including the topology of the free surface,void ratio distribution ahead of the tool,spatio-temporal evolution of the reaction forces and abrasive wear behavior are evaluated.

A Stabilized Crank-Nicolson Mixed Finite Element Method for Non-stationary Parabolized Navier-Stokes Equations

In this study, a time semi-discrete Crank-Nicolson （CN） formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element （SCNMFE） formulation based on two local Gauss integrals and parameter- free with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.

Geometric nonlinear analysis of large rotation behavior of a curved SWCNT

Nanotubes form clusters and are found in curved bundles in nano-tube films and nanocomposites.Separation phenomenon is sus-pected to occur in these curved bundles.In this study,the deformation of a single-wall carbon nanotube(SWCNT)interacting with curved bundle nanotubes is analyzed.It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes.A new method of model-ing geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method(CFEM)formulation,combined with small deformation beam theory,with the inclusion of axial force.Current developed CFEM method overcomes the limitation of linear Finite Element Method(FEM)formulation regarding large rotations and deformations of carbon nanotubes.This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregula-rities in the electronic transport properties of adsorbed nanotubes in nanocomposites.

Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

We propose a new Absorbing Boundary Condition(ABC)for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E.Taylor and which does not depend on the geometry of the surface bearing the ABC.By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions,we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition.We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.