Hydroelastic analysis of insulation containment of LNG carrier by global–local approach

The insulation containment of liquefied natural gas (LNG) carriers is a large‐sized elastic structure made of various metallic and composite materials of complex structural composition to protect the heat invasion and to sustain the hydrodynamic pressure. The goal of the present paper is to present a global–local numerical approach to effectively and accurately compute the local hydroelastic response of a local containment region of interest. The global sloshing flow and hydrodynamic pressure fields of interior LNG are computed by assuming the flexible containment as a rigid container. On the other hand, the local hydroelastic response of the insulation containment is obtained by solving only the local hydroelastic model in which the complex and flexible insulation structure is fully considered and the global analysis results are used as the initial and boundary conditions. The interior incompressible inviscid LNG flow is solved by the first‐order Euler finite volume method, whereas the structural dynamic deformation is solved by the explicit finite element method. The LNG flow and the containment deformation are coupled by the Euler–Lagrange coupling scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

On the geometric factors in fractured media

Abstract

In double‐porosity and multiple continuum models the fractured rock domain can be simplified as two overlapping continua, one for the matrix block system and the other for the fracture network. In this case, it is necessary to define an exchange term accounting for the transfer of fluid and solute masses between the two continua. A newly derived geometric parameter appears in the fluid exchange term, and is valid for any point‐centered block. The geometric parameter is more general and has a clear physical meaning. It is a function of both the shape and the size of the matrix block and agrees well with the double porosity model. The geometric center and conductance of the element is different under the quasi‐steady state compared to the steady state. Quasi‐steady condition is more suitable than steady state condition for modeling fractured media.     

A local thermomechanical model of friction for computing structures under extreme loading conditions

A multiscale thermomechanical model of friction is proposed for metallic interfaces submitted to extreme loading conditions with large sliding velocities ( [v] > 100 ms^?1) and high contact pressures (P > 1 GPa). This model decomposes the friction problem into a global multidimensional structural problem and a local interface subproblem. At global scale, the structure behavior is governed by an elastoplastic model in large strains, and thermal conduction is neglected. The local model describes the micrometric scale and the underlying thermomechanical mechanisms: mechanical hardening, frictional heating, and plastic work. Using dimensional and asymptotic analysis, the corresponding set of equations at local scale is simplified and reduces to a one‐dimensional quasistatic thermoelastoplastic friction model. It is solved locally at each global point by a finite differences subgrid model using a nonlinear time‐implicit solver. This solver is coupled to a time‐explicit Lagrangian hydrocode used at the global structural scale. The coupling strategy between the solvers is force‐based: the frictional stress is evaluated at the local scale by our multiscale friction model and transferred to the global model that can then predict local velocity corrections. This coupling strategy has been successfully tested on real‐life cases. Copyright © 2011 John Wiley & Sons, Ltd.     

A computational model for fracturing porous media

This paper presents a new computational model for simulating a fracturing process in a porous medium using the finite element method. Two independent numerical techniques are used for describing this process. The partition of unity method is used for describing the fracturing process, and the double porosity model is used for describing the resulting fluid flow. A key feature of the model is the coupling of these two independent numerical techniques, which provide the means for a better simulation of the involved physical and mechanical processes. The paper focuses on the numerical formulation of the model. The capability of the model is illustrated by means of numerical examples, which examine the behaviour of a 1D porous medium under different boundary conditions. The numerical results show that the very complicated physical and mechanical processes of the fracturing porous media can be simulated properly and efficiently. Copyright © 2006 John Wiley & Sons, Ltd.     

Coupled thermo/hydro/chemical/mechanical model for unsaturated soils—Numerical algorithm

This paper presents the implementation of a numerical algorithm for a new coupled thermal–hydraulic–chemical–mechanical model for unsaturated soil. A brief treatment of the theoretical development of the coupled model is presented first, with specific attention to the multi‐component chemical transport theory and its cross couplings with other primary variables. The system of coupled equations is based on a mechanistic approach with conservation of mass or energy equations defining the flow behaviour and a stress–strain equilibrium equation defining the mechanical behaviour. The geochemical interactions are incorporated by linking a geochemical model with the system of coupled flow and deformation equations. Two coupling strategies, namely, sequential non‐iterative and sequential iterative approaches are incorporated to link the multi‐component chemical transport equation with geochemical interactions. The model's ability is then demonstrated via a series of 1D examples, which consider complex coupling scenarios involving all the primary variables. Specifically, the effects of multi‐component precipitation/dissolution and ion exchange reactions in a variable thermal–hydraulic–mechanical field are considered. The numerical efficiency of the model is also analysed based on these examples. It is concluded that the model not only provides a stable solution but is able to produce results that are qualitatively consistent with observed behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

The Asymptotic Expansion Load Decomposition elastoplastic beam model

A new higher‐order elastoplastic beam model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher‐order elastic beam model using the asymptotic expansion method. This model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the beam. In order to capture the effect of plasticity on the structure, the present elastoplastic model considers the plastic strain as an eigenstrain imposed on the structure, and new degrees of freedom are added on the fly into the kinematics during the incremental‐iterative process. The radial return algorithm of J₂ plastic flow is used. Because of the constant evolution of beam kinematics, the Newton‐Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever beam loaded at its free extremity is presented and compared to a three‐dimensional reference solution. The beam model shows satisfying results even at a local scale and for a significantly reduced computation time.     

The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction

The paper introduces a weighted residual‐based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple‐flow‐immersed solid objects. The fluid flow is described by the incompressible Navier–Stokes equations. The current configuration of the thin structure of linear elastic material with non‐linear kinematics is mapped to the flow using the zero iso‐contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space–time finite element discretization of the domain. Interfacial constraints of the multi‐field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid–structure systems. Embedding a thin structure into a flow results in non‐smooth fields for the fluid. Based on the concept of the extended finite element method, the space–time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space–time (EST) method. Numerical examples of fluid–structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail. Copyright © 2007 John Wiley & Sons, Ltd.     

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.     

Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

The numerical modelling of interacting acoustic media by boundary element method–finite element method (BEM–FEM) coupling procedures is discussed here, taking into account time‐domain approaches. In this study, the global model is divided into different sub‐domains and each sub‐domain is analysed independently (considering BEM or FEM discretizations): the interaction between the different sub‐domains of the global model is accomplished by interface procedures. Numerical formulations based on FEM explicit and implicit time‐marching schemes are discussed, resulting in direct and optimized iterative BEM–FEM coupling techniques. A multi‐level time‐step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time‐marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating the potentialities and robustness of the proposed methodologies. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite element implementation of non‐linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control

Implicit stress integration algorithms have been demonstrated to provide a robust formulation for finite element analyses in computational mechanics, but are difficult and impractical to apply to increasingly complex non‐linear constitutive laws. This paper discusses the performance of fully explicit local and global algorithms with automatic error control used to integrate general non‐linear constitutive laws into a non‐linear finite element computer code. The local explicit stress integration procedure falls under the category of return mapping algorithm with standard operator split and does not require the determination of initial yield or the use of any form of stress adjustment to prevent drift from the yield surface. The global equations are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatically the coarse load increment size. The proposed numerical procedure is illustrated here through the implementation of a set of elastoplastic constitutive relations including isotropic and kinematic hardening as well as small strain hysteretic non‐linearity. A series of numerical simulations confirm the robustness, accuracy and efficiency of the algorithms at the local and global level. Published in 2001 by John Wiley & Sons, Ltd.     

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

In this study, the dislocation‐based model is developed to study the interaction between time‐harmonic elastic waves and multiple interface cracks in 2 bonded dissimilar piezoelectric layers. In this model, cracks are represented by a distribution of so‐called electro‐elastic dislocations whose density is to be determined by satisfying the boundary conditions. Using the Fourier transform, this formulation leads to 2 singular integral equations, which can be solved numerically for the densities of electro‐elastic dislocations on a crack surface. The formulation is used to determine dynamic field intensity factors for multiple interface cracks without limitation of number of cracks. The dynamic field intensity factors are then calculated for both permeable and impermeable crack, and finally, numerical results are presented to illustrate the variation of these quantities with the electromechanical coupling, crack spacing, and the frequency of loading.     

A 3D anisotropic elastoplastic‐damage model using discontinuous displacement fields

This paper is concerned with the development of constitutive equations for finite element formulations based on discontinuous displacement fields. For this purpose, an elastoplastic continuum model (stress–strain relation) as well as an anisotropic damage model (stress–strain relation) are projected onto a surface leading to traction separation laws. The coupling of both continuum models and, subsequently, the derivation of the corresponding constitutive interface law are described in detail. For a simple calibration of the proposed model, the fracture energy resulting from the coupled elastoplastic‐damage traction separation law is computed. By this, the softening evolution is linearly dependent on the fracture energy. The second part of the present paper deals with the numerical implementation. Based on a local and incompatible additive split of the displacement field into a continuous and a discontinuous part, the parameters specifying the jump of the displacement field are condensed out at the material level without employing the standard static condensation technique. To reduce locking effects, a rotating localization zone formulation is applied. The applicability and the performance of the proposed numerical implementation is investigated by means of a re‐analysis of a two‐dimensional L‐shaped slab as well as by means of a three‐dimensional ultimate load analysis of a steel anchor embedded in a concrete block. Copyright © 2004 John Wiley & Sons, Ltd.     

A moving superimposed finite element method for structural topology optimization

Level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. In this paper, a dynamic implicit boundary‐based moving superimposed finite element method (s‐version FEM or S‐FEM) is developed for structural topology optimization using the level set methods, in which the variational interior and exterior boundaries are represented by the zero level set. Both a global mesh and an overlaying local mesh are integrated into the moving S‐FEM analysis model. A relatively coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. In numerical integration using the Gauss quadrature rule, the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes. A double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co‐ordinate systems. An element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency. A simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint. A physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated PDE solving procedure. The proposed moving S‐FEM is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems. For the classical elasticity problems in the literature, the present S‐FEM can achieve numerical results in good agreement with those from the theoretical solutions and/or numerical results from the standard FEM. For the minimum compliance topology optimization problems in structural optimization, the present approach significantly outperforms the well‐recognized ‘ersatz material’ approach as expected in the accuracy of the strain field, numerical stability, and representation fidelity at the expense of increased computational time. It is also shown that the present approach is able to produce structures near the theoretical optimum. It is suggested that the present S‐FEM can be a promising tool for shape and topology optimization using the level set methods. Copyright © 2005 John Wiley & Sons, Ltd.     

基于分形的三维粗糙表面弹塑性接触力学模型与试验验证

基于分形几何理论,利用双变量的Weierstrass-Mandelbrot函数模拟三维分形粗糙表面,建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数,获得了总接触载荷和真实接触面积之间的关系式。计算结果表明:单个微凸体的临界接触面积与其尺寸相关,随着微凸体等级的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的6个等级微凸体相关,其余微凸体基本上对整个粗糙表面的力学性能影响很小。最后对粗糙表面的接触力学性能进行了试验测试,验证了该模型的合理性与正确性。     

Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling

An iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid–solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non‐linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non‐linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain. Copyright © 2005 John Wiley & Sons, Ltd.     

A three‐dimensional element‐free Galerkin elastic and elastoplastic formulation

A small strain, three‐dimensional, elastic and elastoplastic Element‐Free Galerkin (EFG) formulation is developed. Singular weight functions are utilized in the Moving‐Least‐Squares (MLS) determination of shape functions and shape function derivatives allowing accurate, direct nodal imposition of essential boundary conditions. A variable domain of influence EFG method is introduced leading to increased efficiency in computing the MLS shape functions and their derivatives. The elastoplastic formulations are based on the consistent tangent operator approach and closely follow the incremental formulations for non‐linear analysis using finite elements. Several linear elastic and small strain elastoplastic numerical examples are presented to verify the accuracy of the numerical formulations. Copyright © 1999 John Wiley & Sons, Ltd.     

On the undrained and drained hydraulic fracture splits

The simulation of hydraulic fracturing (HF) involves the solution of a hydro-mechanically coupled system. This article presents a new iterative sequential coupling algorithm, the undrained HF split, that improves the simulation of HFs in impermeable media. A poromechanics analogy is used to derive a stable split for the hydro-mechanically coupled system in which the mechanical subproblem is solved first. The proposed undrained HF split is applied to the simulation of cohesive HFs in an impermeable elastic medium. The cubic law is used as the constitutive model for simulating fluid flow in fractures. A minimum hydraulic aperture is assumed in the cohesive tip zone, where the mechanical aperture smoothly vanishes. While general in its nature, the undrained HF splitting scheme is employed within the context of a two-dimensional eXtended finite element model for the fractured solid, and a regular finite element model for fluid in the fracture. The undrained HF split is successfully used to simulate self-similar plane strain HFs as well as the propagation of HFs from a wellbore under anisotropic stress conditions. Fracture trajectories and local alteration of stress field are investigated. The solution of the undrained HF split converges to the same solution as the fully coupled model, whereas the commonly used P→W sequential algorithm, referred to in this article as the drained HF split, generates spurious oscillations and fails to converge in many problems. The undrained HF split is shown to be stable and robust in applications where the drained HF split is unstable.     

An analysis of a new class of integration algorithms for elastoplastic constitutive relations

An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.     

钢筋混凝土框架结构弹塑性数值子结构分析方法

大型复杂土木工程结构在地震作用下失效破坏可能由部分关键构件严重损伤破坏导致,而大部分构件仍处于弹性或小变形状态。该类结构的地震损伤和破坏全过程分析涉及超大规模系统强非线性动力分析,目前尚缺乏能很好兼顾效率和精度的计算理论,基于此,该文提出一种新型高效且实用的弹塑性数值子结构理论和计算方法,将大型复杂结构系统的大规模非线性计算问题转化为整体结构适度规模的线弹性分析和数量与规模均较小的局部隔离子结构非线性分析,其中,线弹性整体结构刚度矩阵的集成及LU三角分解仅需进行一次,大大提高计算效率;少数屈服构件的子结构非线性分析采用精细化有限元模型或不同类型单元模型,精确模拟构件局部损伤破坏机理,有效提高结构整体的计算精度。最后通过对一榀平面钢筋混凝土框架结构进行地震动力弹塑性数值子结构方法分析,验证其高效性与精确性。     

A two‐scale approximation of the Schur complement and its use for non‐intrusive coupling

This paper presents a two‐scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (i.e. element strips) and global (i.e. homogenized) contributions. This approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure; the strategy consists in creating a local model that contains the desired features of the concerned region and then substituting it into the global problem by the means of a non‐intrusive solver coupling technique adapted from domain decomposition methods. Using the two‐scale approximation of the Schur complement as a Robin condition on the local model enables to reach high efficiency. Examples include a large 3D problem provided by our industrial partner Snecma. Copyright © 2011 John Wiley & Sons, Ltd.