A new element for analyzing large deformation of thin Naghdi shell model. Part 1: Elastic

One of the best approaches for modeling large deformation of shells is the Cosserat surface. However, the finite-element implementation of this model suffers from membrane and shear locking, especially for very thin shells. The basic assumption of this theory is that the mid-surface of the shell is regarded as a Cosserat surface with one inextensible director. In this paper, it is shown that by constraining the director vector normal to the mid-surface, besides very good and accurate results, shear locking is also eliminated. This constraint is in fact a limiting analysis of the Cosserat theory in which Kirichhoff’s hypothesis is enforced. Numerical solution is performed using nine-node isoparametric element. The principal of virtual work is used to obtain the weak form of the governing differential equations and the material and geometric stiffness matrices are derived through a linearization process. The validity and the accuracy of the method are illustrated by numerical examples.     

Numerical Locking Problems for Hyperbolic Equations

We investigate a time-dependent model concerning the “locking phenomenon,” namely a model for three-dimensional clamped curved rods. We show that the convergence of the numerical schemes is independent of the discretization parameters and the thickness of the rod. We present corresponding numerical experiments.     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

Optimum design of laminated composite plates under dynamic excitation

An integrated model for optimum weight design of symmetrically laminated composite plates subjected to dynamic excitation is presented in this work. Optimum design procedure based on flexibility and strength criteria is presented. The objective is to determine the optimum thicknesses of the laminate layers and its optimum orientations without exhibiting any failure according to Tsai-Wu failure criterion. The finite element method, based on Mindlin plate theory, is used in conjunction with an optimization method in order to determine the optimum design. Newmark algorithm, as an implicit time integration scheme, is used to discretize the time domain and calculate the transient response of the laminated composite plate. Exterior penalty method is exploited for the constrained minimization procedure. Fletcher-Powell algorithm is used for the unconstrained minimization process. To verify the capability and efficiency of the proposed model, three examples are solved. The examples deal with flexibility and stress constraints for different boundary conditions under various dynamic excitations.     

Numerical modeling of free field vibrations due to pile driving using a dynamic soil-structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field, where deformations are relatively small, a linear elastic constitutive behavior is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model using a subdomain formulation. The results show that, in the near field, the response of the soil is dominated by a vertically polarized shear wave, whereas in the far field, Rayleigh waves dominate the ground vibration and body waves are importantly attenuated. Finally, the computed ground vibrations are compared with the results of field measurements reported in the literature.     

A reduced constraint finite element method for shell problems

We propose and analyze an finite element method for the Nagdhi shell model, based on rectangular elements. We show that for the bending-dominated case, assuming sufficient smoothness on the solution, the method is locking free in terms of both and , as the thickness of the shell tends to zero. Our results are established under the assumption that the geometrical coefficients appearing in the model are piecewise polynomial functions.

     

奇异摄动Darcy-Stokes问题的一个矩形有限元

构造了一个新的非协调的矩形单元,分析了单元对奇异摄动Darcy-Stokes问题的稳定性,给出了有限元误差分析结果.用数值实验验证了理论分析结果.     

Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem

In this work, we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a non-monotone relation between the tangential stress and the tangential velocity. This leads to a system of second-order inclusion for displacement and a parabolic equation for temperature. We provide a fully discrete approximation of the problem and find optimal error estimates without any smallness assumption on the data. The theoretical result is illustrated by numerical simulations.     

An enhanced finite volume method to model 2D linear elastic structures

This paper details the evaluation and enhancement of the vertex-centred finite volume method for the purpose of modelling linear elastic structures undergoing bending. A matrix-free edge-based finite volume procedure is discussed and compared with the traditional isoparametric finite element method via application to a number of test-cases. It is demonstrated that the standard finite volume approach exhibits similar disadvantages to the linear Q4 finite element formulation when modelling bending. An enhanced finite volume approach is proposed to circumvent this and a rigorous error analysis conducted. It is demonstrated that the developed finite volume method is superior to both standard finite volume and Q4 finite element methods, and provides a practical alternative to the analysis of bending-dominated solid mechanics problems.     

Prediction of the dynamic response of a mini-cantilever beam partially submerged in viscous media using finite element method

In this work, the use of mini cantilever beams for characterization of rheological properties of viscous materials is demonstrated. The dynamic response of a mini cantilever beam partially submerged in air and water is measured experimentally using a duel channel PolyTec scanning vibrometer. The changes in dynamic response of the beam such as resonant frequency, and frequency amplitude are compared as functions of the rheological properties (density and viscosity) of fluid media. Next, finite element analysis (FEA) method is adopted to predict the dynamic response of the same cantilever beam. The numerical prediction is then compared with experimental results already performed to validate the FEA modeling scheme. Once the model is validated, further numerical analysis was conducted to investigate the variation in vibration response with changing fluid properties. Results obtained from this parametric study can be used to measure the rheological properties of any unknown viscous fluid.     

Detonation-driven fracture in thin shell structures: Numerical studies

Detonation-driven fracture of thin structures is studied numerically by a 3D discrete crack meshfree method. These types of failure mechanisms play an important role in pipes and vessels. I therefore proposed a three-dimensional meshfree method and an efficient discrete crack model to describe crack propagation. The method is based on separation of particles similar to the visibility method but its implementation is more efficient. I assume here through-thickness cracks though the method can be extended to crack growth in arbitrary directions. The load is applied as travelling pressure wave obtained from pure fluid simulation in accordance with experimental measurements. Numerical results to experimental data show good agreement.     

Nonlinear analysis of elastic thin-walled shell structures

Theoretical principles, methodology and algorithms presented herein are to analyze and design the elastic thin-walled engineering structures and components, with emphasis on the important nonlinear behavior. The methodology of the consequent analysis of single-parametric nonlinear problems is applied to structural syntheses. The numerical algorithm for this analysis is based on the parameter continuation methods and the “control parameter subspace changing”. The effectiveness of the proposed approach is illustrated through several examples in thin-walled structures.     

The study of the dynamic contact in ultrasonic motor

In this paper, we consider a mathematical model which describes the dynamic contact between an elastic body and an obstacle. The process is assumed to be dynamic and the contact is modeled with the normal compliance. We present a variational formulation of the problem and prove the existence and the uniqueness of a weak solution. An efficient numerical method is presented to analyze this dynamic contact. This approach exploits the augmented Lagrangian concept and a special time integration algorithm. This is exploited to study the dynamic contact between the rotor and the stator inside an ultrasonic motor SHINSEI USR 60. Numerical results are presented and show the interest of this method to forecast the origin of the principal failure mode of this motor.     

Global stability for nonlinear dynamic equations with variable coefficients

We give sufficient conditions under which the trivial solution of a nonlinear dynamic equation with variable coefficients is globally asymptotically stable, for arbitrary time scales unbounded above.     

A finite-element mechanical contact model based on Mindlin-Reissner shell theory for a three-dimensional human body and garment

Efficient numerical methods for describing a garment’s mechanical behavior during wear have been identified as the key technology for garment simulation. This paper presents a finite-element mechanical contact model based on Mindlin-Reissner shell theory for a three-dimensional human body and garment. In this model, the human body and the garment are meshed as basic contact cells, these contact cells between the human body and the garment are defined as the contact pair to describe the contact relationship, and the mathematical formulation of the finite-element model is defined to describe the strain-stress performance of the three-dimensional human body and garment system. By using the solution given by the computer code and the programs specifically developed, the calculations of the mechanics in the basic cells of the human body and the garment have been able to be carried out. The simulation results show that the model of rationality, a good simulation results and simulation efficiency.     

Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.     

Discrete finite element characterizations of source fields for volume and boundary constraints in electromagnetic problems

The consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields. Such source fields are first defined for both volume and boundary constraints in static electromagnetic models. Then, automatic procedures are proposed to conveniently and efficiently characterize discrete source fields, with regard to their use in finite element formulations, their supports, their direct expression requiring no pre-computation, and their associated constraints. Two application examples are proposed to illustrate the approach.     

A posteriori error estimator for finite volume methods

In this paper, first we discuss a technique to compare finite volume method and some well-known finite element methods, namely the dual mixed methods and nonconforming primal methods, for elliptic equations. These both equivalences are exploited to give us a posteriori error estimator for finite volume methods. This estimator is explicitly given, easy to compute and asymptotically exact without any regularity of the solution in unstructured grids.     

Strict stability criteria for dynamic systems on time scales

In this paper we obtain sufficient conditions for strict stability to hold for dynamic systems on time scales.     

服从OldroydB型微分模型的粘弹性流体问题的数值解法

本文对服从OldroydB型微分模型的粘弹性流体问题给出了一种数值逼近算法．该算法对压力方程采用标准混合有限元方法,对速度方程采用并行非重叠区域分解方法和特征线法．这种并行算法在子区域上用Galerkin方法,通过积分平均方法显式地给出内边界的数值流．在本文最后还给出了该算法的最优L^2。一误差估计．