AN IMPLICIT SERIES PRECISE INTEGRATION ALGORITHM FOR STRUCTURAL NONLINEAR DYNAMIC EQUATIONS

Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these algorithms. If the inversion of the matrix doesn‘t exist or isn‘t stable, the precision and stability of the algorithms will be affected. An explicit series solution of the state equation has been presented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented.The algorithm is more precise and stable than the explicit series solution and isn‘t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the effectiveness of the algorithm.     

THEORY AND REFINED THEORY OF ELASTICITY FOR TRANSVERSELY ISOTROPIC PLATES AND A NEW THEORY FOR TNICK PLATES

A theory of elasticity for the bending of transversely isotropic plates has been developed from the basic equations of elasticity in terms of displacements for transversely isotropic bodies, which takes into account the loads distributed over the surfaces of the plates. Based on this theory, a refined theory of plates which can satisfy three boundary conditions along each edge of the plates and a new theory of thick plates are established. The solution of the refined theory for simply supported polygonal plates has been obtained; and its numerical result is very close to the exact solution of the three-dimensional theory of elasticity. A systematic comparison with the former theories of thick plates shows that the present theory of thick plates is closest to the result of the theory of elasticity.     

Finite element analysis for consolidation in interaction between structure and saturated soil foundation

The consolidation analysis of interaction between structure and saturated soil foundation is discussed. With the use of substructure technique, the structure is condensed onto the interface of the soil, and then the consolidation governing equations to describe the interaction between soil and structure are derived, The solution with non-iterative algorithm is proposed in this paper. The pressure Master-Slave relation method is used to deal with the non-permeability conditions on soil boundaries. A numerical example is illustrated. Based on this paper, the interactive consolidation analysis between large structure and soil has been more practical.     

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.     

Laminar assisting mixed convection heat transfer from a vertical isothermal cylinder moving in water at low temperatures

In all studies concerning laminar mixed convection along a vertical isothermal moving cylinder a linear relationship between fluid density and temperature has been used and viscosity and thermal conductivity have been considered constant. However, it is known that the density-temperature relationship for water is non-linear at low temperatures and viscosity and thermal conductivity are functions of temperature. In this study the problem of water laminar mixed convection along a vertical isothermal moving cylinder has been investigated in the temperarure range between 20 °C and 0 °C taking into account the temperature dependence of μ, k and ρ. The results are obtained with the numerical solution of the boundary layer equations. The variation of μ, k and ρ with temperature has a strong influence on mixed convection characteristics.     

Analysis of phase transformation from austenite to martensite in NiTi alloy strips under uniaxial tension

Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation.This work presents an analysis using the theory of phase transfor- mation.The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered.Governing equations for the phase transformation are derived.The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique,real and physically acceptable solution.The equa- tions are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress,the stresses and strains inside both anstenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.     

Dynamic buckling of stiffened plates under fluid-solid impact load

A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.     

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

An iterative parallel algorithm of finite element method

In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.     

以u—U形式方程为基础的结构—饱和土壤相互作用的固结有限元分析

提出用u-U形式方程对饱和土固结问题进行分析,对于结构则采取多重子结构技术实现向饱和土交界面上的凝聚,从而建立了结构与饱和土相互作用的固结控制方程。文中给出了方程的求解方案。文末给出了数值算例。本文的工作已在DIASS程序系统中实现。     

Moving‐boundary analysis of net vapor generation point in a steam generator

This paper deals with the study of the dynamics of net vapor generation point in the boiling channel of the steam generator of Kaiga‐1 nuclear power plant. The dynamics has been studied by perturbing liquid velocity at the inlet of boiling channel with a step function and heating rate with a ramp function. Both finite volume method (FVM) and finite difference method (FDM) have been applied to solve the model equations that have been developed to predict boiling boundary. The effect of thermal non‐equilibrium conditions on subcooled boiling has been taken into consideration. A comparative study of the two methods has been carried out based on the analytical solution of the equations. The study shows that at higher system frequency, increasing number of computational grids increase the accuracy of numerical solutions using FVM while FDM fails to achieve the same. The superiority of FVM over FDM for the problem has also been confirmed by grid convergence analysis. An attempt has also been made to find the analytical solution of the effect of change of heat input on boiling boundary, which is an essential part of computations for the simulation of startup and shutdown of the steam generator. Copyright © 2008 John Wiley & Sons, Ltd.     

无穷域势流问题的有限元／差分线法混合求解

提出了一种将有限元和差分线法相结合求解无穷域势流问题的算法。用两同心圆将求解域划分为存在重叠的有限和无限两个区域,在有限和无限域上分别用有限元和差分线法求解Laplace方程边值问题。用差分线法推导出的关系式修正有限元方程,求解该方程组从而得到原问题的解。本算法将求解无穷域问题转化为代数特征值问题和有限域内线性方程组的...     

Numerical analysis of one-dimensional nonlinear large-strain consolidation by the finite element method

The nonlinear partial differential equation model of Gibson et al. which governs one-dimensional large-strain consolidation is solved numerically using a semi-discrete formulation involving a Galerkin weighted residual approach. The use of quadratic Lagrange basis functions usually complicates the task of solving the system of time-dependent ordinary differential equations that are obtained with the semi-discrete Galerkin procedure. However, an efficient algorithm has been discovered yielding the advantages of quadratic interpolation without undue computational burden.Although considerable effort has already been made to solve the PDE of large-strain consolidation by numerical methods, a satisfactory set of benchmarks is still needed to assess accuracy. To fill this need, three procedures are reported which allow numerical solutions of the large-strain model to be reliably evaluated. One involves the use of perturbation methodology to provide a solution when only self-weight effects are present. A second utilizes an analytical solution developed by Philip when self-weight effects are absent and the third involves the exact calculation of the discharge flux through the upper boundary of a deposit consolidating through self-weight effects alone. All three are restricted to early-time consolidation and are illustrated in the context of the finite element method.     

非线性大变形问题边界元分析的自校正方法

针对用增量法求解非线性方程解的漂移问题，在非线性问题边界元法计算中建立了自我校正方法，对在拖带坐标上建立的增量形式的基本方程，引入Ｌａｎｇｒａｎｇｅ校正因子，以全量形式的基本方程作为其辅助方程，在此基础上导出含校正项的边界积分方程，边界元自我校正方法的建立有效地保证了在非线性问题的计算中最终收敛在其解附近，提高了计算精度和运算效率。     

Integrated numerical model for vegetated surface and saturated subsurface flow interaction

The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.     

Solving material nonlinear structural problems by a finite analytic method in local coordinates

The purpose of this paper is to develop a finite analytic (FA) numerical solution for the elasto-plastic problem of the total theory. Schemes for the FA method in local coordinates for solving non-linear governing equations in the form of Navier equations are derived, which can be utilized to solve the problem in a domain of arbitrary geometry. Numerical illustration shows that the schemes are effective and practical.     

Footbridge between finite volumes and finite elements with applications to CFD

The aim of this paper is to introduce a new algorithm for the discretization of second‐order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier–Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright © 2001 John Wiley & Sons, Ltd.