Analysis of chloride diffusion in concrete structures for prediction of initiation time of corrosion using a new meshless approach

In this paper, a finite point method (FPM) is developed and adopted for solving the chloride diffusion equation for prediction of service life of concrete structures and initiation time of corrosion of reinforcements. Diffusion of chloride ions is generally assumed to follow the Fick’s second law. FPM is a truly meshless method which uses a moving least square approximation within a collocation strong form for solving the governing differential equation. Several 1D and 2D problems are solved using FPM and the results are compared with the analytical solution, classical finite element and finite difference methods, and weak form meshless based element free Galerkin method.     

Response of functionally graded cylindrical shells under moving thermo-mechanical loads

The transient thermoelastic analysis of functionally graded (FG) cylindrical shells under moving boundary pressure and heat flux is presented. The material properties are assumed to be temperature-dependent and graded in the radial direction. The hyperbolic heat conduction equations are used to include the influence of finite heat wave speed (i.e., the non-Fourier effect). To benefit from the high accuracy and low computational efforts of the differential quadrature method (DQM) in conjunction with the effectiveness of the finite element method (FEM) in general geometry, loading and systematic boundary treatment, a combination of these methods is employed to discretize the governing equations in the spatial domain. The resulting system of differential equations is solved using Newmark's time integration scheme in the temporal domain. The presented formulation and method of solution are validated by showing their fast rate of convergence and by comparing the results, in the limit cases, with those obtained using the commercial finite element package ANSYS and some other available solutions in the literature. Then, the effects of different geometrical, material and load parameters on the transient thermoelastic behavior of the FG cylinders under moving mechanical and thermal loads are studied.     

A simple time domain calculation method for transient heat transfer models

This paper presents a simple time domain calculation method to derive thermal response factors and conduction transfer conduction (CTF) coefficients of finite differential models for estimating transient heat transfer through building structures. It is developed on the basis of converting the matrix exponential function, which is a part of the solution of the state equation established from the finite differential equations of building finite differential models, to matrix polynomial. The thermal response factors and CTF coefficients can be easily derived from the matrix polynomial with simple arithmetic and integral in time domain. This method avoids the time-consuming root-finding process of conventional methods and the computation of all the internal temperature of the finite differential model, while utilizing the advantage of the thermal response factors/CTF coefficients which relate the desired outputs at a moment to the previous inputs through a set of coefficients. Various case studies were conducted to validate the performance of this time domain calculation method in calculating the thermal response factors and CTF coefficients of various order finite differential models.     

SIMULATING WATER MOVEMENT AND ITS UPTAKE BY PLANT ROOTS IN UNSATURATED ZONES

Existing mathematical models that simulate water movement and contaminant transport in unsaturated zone do not take into account the water uptake by plant crop roots resulting in an error in the prediction of water flux and, thereby, contaminant concentration. Moreover the application of these models is often limited due to the lack of easily accessible and representative soil hydraulic properties, like moisture retention characteristic and unsaturated hydraulic conductivity. In this study, a mathematical model is developed for simulating water movement in unsaturated zones by integrating the one‐dimensional transient unsaturated water flow equation (Richard's equation) with a root water extraction term (sink), and also incorporates pedo‐transfer functions (PTF) for estimating soil hydraulic properties. The governing non‐linear partial differential equation is solved numerically by the implicit finite difference method using Picard's iterative technique, the formulation has been illustrated by a characteristic example.     

Velocity-based time-discontinuous Galerkin space-time finite element method for elastodynamics

A velocity-based single-field Space-Time Finite Element Method (v-ST/FEM) is devised within the framework of the time-discontinuous Galerkin method for an elastodynamics problem. The new method uses finite elements for both space and time domains, and reduces the size of the resulting linear system to be solved in each time step compared to the two-field formulation. In v-ST/FEM, the trial functions for the velocity field are continuous in space and discontinuous in time, while the test functions are continuous in both space and time. The displacement and stress fields are computed in a post-processing step using the time-integration process which explicitly includes the velocity field. Accordingly, the displacement-velocity compatibility condition and the continuity of the displacement field in time are strongly imposed in the displacement-velocity-based two-field formulation. In this way, a velocity-based single-field weak formulation is derived from the two-field formulation. The present method is found to be unconditionally stable and third-order accurate. Following a review of the space–time finite element literature, the general theoretical development and formulation aspects of the present methodology are demonstrated. Several numerical examples are given to show the computational performance of the proposed scheme.     

Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams

The classical Vlasov theory for torsional analysis of thin-walled beams with open and closed cross-sections can be generalized by including distortional displacement fields. We show that the determination of adequate distortional displacement fields for generalized beam theory (GBT) can be found as part of a semi-discretization process. In this process the cross-section is discretized into finite cross-section elements and the axial variation of the displacement functions are solutions to the established coupled fourth order differential equations of GBT. We use a novel finite-element-based displacement approach in combination with a weak formulation of the shear constraints and constrained wall widths. The weak formulation of the shear constraints enables analysis of both open and closed cell cross-sections by allowing constant shear flow. We use variational analysis to establish and clearly identify the homogeneous differential equations, the eigenmodes, and the related homogeneous solutions. The distortional equations are solved by reduction of order and solution of the related eigenvalue problem of double size as in non-proportionally damped structural dynamic analysis. The full homogeneous solution is given as well as transformations between different degree of freedom spaces. This new approach is a considerable theoretical improvement, since the obtained GBT equations found by discretization of the cross-section are now solved analytically and the formulation is valid without special attention also for closed single or multi-cell cross-sections. Further more the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.     

寒区隧道温度场、渗流场和应力场耦合问题的非线性分析

首先根据传热学、渗流理论及冻土力学提出了带相变的温度场、渗流场和应力场耦合问题的数学力学模型及其控制方程。然后应用伽辽金法导出了这一问题的有限元计算公式。最后给出了一寒区隧道考虑渗流和冻胀时的温度场和应力场算例。算例表明冻胀力对隧道衬砌应力的影响很大,应充分考虑这一因素的影响。     

基于混合近似法的纤维梁单元非线性求解方法#br#

环境荷载作用下土木工程结构往往产生较大的非线性变形,包括材料非线性和几何大变形两部分,而两者非线性问题的数值求解往往需要花费高昂的计算代价。隔离非线性有限元法是将材料应变分解为弹性与塑性两部分,在控制方程中实现刚度矩阵的弹塑性分离,使用Woodbury公式进行非线性求解。目前,该方法仅用于求解局部材料非线性问题。文章基于隔离非线性有限元法,推导同时考虑材料和几何非线性（简称混合非线性）的纤维梁单元控制方程;依据Woodbury公式和组合近似法的基本理论,提出混合近似法的高效非线性求解方法,并利用时间复杂度理论,对该方法与传统有限元法进行计算效率对比分析;将提出的方法应用于某钢框架结构的地震非线性反应分析,计算结果表明：文中方法可以在求解材料非线性时考虑几何大变形问题,在保证计算精度的同时使计算效率得到明显提升。     

自适应模型缩放非线性动力分析方法

提出一种基于模型损伤的自适应模型降阶动力分析方法。该方法在动力分析的每个分析步中根据损伤分布和损伤程度自适应地定义和调整模型子区域的缩放属性。针对模型缩小子区域，采用模态综合方法对其进行动力缩聚；针对模型放大子区域，采用精细化单元替换原有单元，最终形成混合坐标空间内的结构运动方程，通过求解缩减自由度之后的运动方程来提高计算效率。最后通过一个20层钢框架来验证该方法的有效性和适用性，数值结果表明，自适应模型缩放动力分析方法能够在满足模拟精度要求的同时，显著地提高非线性动力分析的计算效率。     

Natural shape functions of a compressed Vlasov element

To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly.     

Inelastic local buckling of curved plates with or without thickness-tapered sections using finite strip method

This paper addresses the inelastic local buckling of the curved plates using finite strip method in which buckling modes and displacements of the curved plate are calculated using sinusoidal shape functions in the longitudinal direction and polynomial functions in the transverse direction. A virtual work formulation is employed to establish the stiffness and stability matrices of the curved plate whilst the governing equations are then solved using a matrix eigenvalue problem. The accuracy and efficiency of the proposed finite strip model is verified with finite element model using ABAQUS as well as the results reported elsewhere while a good agreement is achieved. In order to illustrate the proposed model, a comprehensive parametric study is performed on the steel and aluminium curved plates in which the effects of curvature, the length of the curved plate as well as circumferential boundary conditions on the critical buckling stress are investigated. The developed finite strip method is also used to determine the buckling loads of the curved plates with thickness-tapered sections as well as critical stresses of the aluminium cylindrical sectors that are subjected to uniform longitudinal stresses.     

Mesh-free Method for Soil-water Coupled Problem within Finite Strain and Its Numerical Validity

A formulation of the Element-Free Galerkin Method (EFG method), i.e., one of the mesh-free/meshless methods developed in the field of computational mechanics for solving partial differential equations, is furnished for consolidation within finite strain and its validity for application to soil-water coupled problems is examined through a numerical analysis. The numerical strategy is constructed to solve a set of governing equations, e.g., the equilibrium for the nominal stress rate and the continuity of pore water, and the numerical discretization of the weak form of the governing equations leads to an updated Lagrangian scheme. The accuracy of the proposed numerical strategy is examined through an analysis of unconfined compression tests and simple shear tests under undrained and plane strain conditions through a comparison of stress paths integrated directly from the Cam-clay model within the framework of finite strain. It is also revealed that the particular type of weight function to be adopted in the moving least-squares (MLS) approximation, even in the same order, can determine the resultant shape functions of the EFG method for both the displacement and the pore water pressure field such that they are smoother than those of the usual FEM. The functions are advantageous in that they avoid spatial instability in the numerical solutions for pore water pressure under undrained conditions appearing in saturated soil column tests, where the shape function of the pore water pressure in the conventional FEM computation is adopted as a lower order than that of the displacement to remedy this type of numerical difficulty. To emphasize the applicability and the feasibility of the mesh-free computation, the consolidation phenomena are demonstrated in the analysis of a punch problem for a soft soil foundation which has stress singularity under both ends of a rigid loading platen for the same problem which Yatomi et al. (1989) solved with FEM.     

Free vibrations of fluid-filled cylindrical shells on elastic foundations

The free vibration characteristics of fluid-filled cylindrical shells on elastic foundations are presented by a semi-analytical finite element method. A shell is discretized into cylindrical finite elements where shell governing equations based shape functions in the longitudinal direction are used instead of the usual simple polynomials. Non-uniformities of the foundations in the circumferential and longitudinal directions are handled by the Fourier series and an element mesh strategy, respectively. The fluid domain is described by the potential flow theory. The hydrodynamic pressure acting on shells is derived from the condition for dynamic coupling of the fluid-structure. The effect of fluid in a shell, shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells is investigated. Numerical results based on the present method converge more rapidly than those obtained by the simple polynomial formulation. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.     

Nonlinear Analysis of Structural Frame Systems by the State-Space Approach

This article presents the formulation and solution of the equations of motion for distributed parameter nonlinear structural systems in state space. The essence of the state-space approach (SSA) is to formulate the behavior of nonlinear structural elements by differential equations involving a set of variables that describe the state of each element and to solve them in time simultaneously with the global equations of motion. The global second-order differential equations of dynamic equilibrium are reduced to first-order systems by using the generalized displacements and velocities of nodal degrees of freedom as global state variables. In this framework, the existence of a global stiffness matrix and its update in nonlinear behavior, a cornerstone of the conventional analysis procedures, become unnecessary as means of representing the nodal restoring forces. The proposed formulation overcomes the limitations on the use of state-space models for both static and dynamic systems with quasi-static degrees of freedom. The differential algebraic equations (DAE) of the system are integrated by special methods that have become available in recent years. The nonlinear behavior of structural elements is formulated using a flexibility-based beam macro element with spread plasticity developed in the framework of state-space solutions. The macro-element formulation is based on force-interpolation functions and an intrinsic time constitutive macro model. The integrated system including multiple elements is assembled, and a numerical example is used to illustrate the response of a simple structure subjected to quasi-static and dynamic-type excitations. The results offer convincing evidence of the potential of performing nonlinear frame analyses using the state-space approach as an alternative to conventional methods.     

变热源强度温度荷载作用下非饱和土中的水分迁移规律研究

给出非饱和土中热能传输和水分迁移的耦合控制微分方程。假定无限介质内热源的存在引起周围多孔介质内温度的瞬态变化和水分的迁移和扩散。利用多重Fourier变换、Laplace变换给出其在变换域上的解,然后利用热源函数法给出瞬时点热源条件下非稳态温度场、体积含水率分布场的解析求解方法。通过在时间域上和空间域上进行积分,建立热源强度随时间变化的球域热源情况下的数值积分求解方法,给出温度场作用下多孔介质内水分迁移的演化规律和分布特征。     

三维轴对称功能梯度材料瞬态热传导问题的自然单元法

为了更有效地求解三维轴对称功能梯度材料瞬态热传导问题,对无网格自然单元法应用于此类问题进行了研究,并发展了相应的计算方法。基于几何形状和边界条件的轴对称性,三维的轴对称问题可降为二维平面问题。为了简化本质边界条件的施加,轴对称面上的温度场采用自然邻近插值进行离散。功能梯度材料特性的变化由高斯点的材料参数进行模拟。时间域上,采用传统的两点差分法进行离散求解,进而得到瞬态温度场的响应。数值算例结果表明,提出的方法是行之有效的,理论及方法不仅拓展了自然单元法的应用范围,而且对三维轴对称瞬态热传导分析具有普遍意义。     

基于场模型的大空间建筑火灾钢构件升温的简化计算方法

高大空间建筑火灾中，热量主要通过热烟气的辐射传热和对流传热方式，向无防火保护层的钢构件表面或钢构件的防火保护层传递，防火保护层再以热传导方式向钢构件表面传递。假定钢构件截面温度均匀分布，将高大空间建筑火灾中的实用空气升温曲线作为构件升温边界条件，对集总热容法建立的热平衡方程求解，得出钢构件在火灾下的温度一时间曲线。为便于工程应用，在钢构件升温影响参数分析的基础上，通过曲线拟舍得出实用的钢构件升温计算公式，为研究大空间钢结构建筑在火灾下的结构全过程反应，提供钢构件升温条件。     

Generalised beam theory-based finite elements for elastoplastic thin-walled metal members

This paper addresses the formulation and validation of GBT-based beam finite elements, intended to analyse the physically non-linear (plastic zone) behaviour of thin-walled metal members. Both stress-based and stress resultant-based elastoplastic formulations are developed. The stress-based formulation is generally more accurate, but the stress resultant-based formulation, which employs the Ilyushin yield function, leads to significant computational savings, namely (i) numeric integration in the through-thickness direction is not required and (ii) constraints to the stress resultant and work-conjugate strain field, typical of linear elastic GBT-type formulations, are straightforwardly enforced. The choice of interpolation functions and the cross-section discretization procedure are also discussed. In order to illustrate the application, provide validation and demonstrate the capabilities of the proposed finite elements, several numerical results are presented and discussed. These results are compared with those obtained with standard 2D-solid and shell finite element analyses.     

梁和框架结构的大变形非线性分析

描述了有限元方法分析梁和框架结构的几何非线性问题,考虑大转动的影响,在有限转动公式的级数展开式中,取二阶近似,从而形成线性刚度矩阵和几何刚度矩阵,推导了大变形情况下梁的本构方程,算例表明：对于较复杂的几何非线性问题,本文提出的方法是有效的。     

Sensitivity study of time delay coefficient of heat transfer formulations for insulated steel members exposed to fire

Heat transfer analysis for an insulated steel member exposed to fire conditions, in general, involves solving a 2D transient conduction equation with well-posed conditions. For design purpose, the current Eurocode 3 provisions adopt a closed-form solution from the SP approach which employs a simplified 1D characteristic heat transfer model. A virtual “time delay” has been incorporated in the analytical solution based on the assumption that the heat capacitance of insulation material is small compared to that of steel section. A sensitivity study is presented in this paper to assess the validity of the time delay coefficient. Results of the study indicate that for insulation with large heat capacitance, the time delay estimation in the SP approach yields significant discrepancy compared against exact solution. An exact formulation of time delay is recommended, which gives accurate results for insulation material with either small or large heat capacitance.