Geometrical nonlinear analysis of structures using residual variables

The capability of nonlinear analysis methods in tracing the equilibrium path depends on how to return to static status. In this paper, some residual factors existed in the iteration steps are employed. By setting the residual load parameter to zero, minimizing its factor and the residual displacement parameter, three novel constraint equations are obtained. The new formulas are proved by numerical examples. All obtained results illustrate the minimum residual load scheme's robustness in comparison with the cylindrical arc-length algorithm and other previous strategies. Moreover, the capacities of new procedures in tracing the load and displacement limit points are assessed.     

Inviscid flow modelling using asymmetric implicit finite difference schemes

Asymmetric spatial implicit high‐order schemes are introduced and, based on Fourier analysis, the dispersion and damping are calculated depending on the asymmetry parameter. The derived schemes are then applied to a number of inviscid problems. For incompressible convection problems the proposed asymmetric schemes (applied as upwind schemes) lead to stable and accurate results. To extend the applicability of the proposed schemes to compressible problems acoustic upwinding is used. In a two‐dimensional compressible flow example acoustic and conventional upwinding are combined. Evaluation of all presented results leads to the conclusion that, of the studied schemes, the implicit fifth order upwinding scheme with an asymmetry parameter of about 0.5 leads to the optimal results. Copyright © 2005 John Wiley & Sons, Ltd.     

泡沫铝夹层结构抗冲击性能的近场动力学模拟分析

针对某光学舱所采用的泡沫铝夹层防护结构在破片冲击下的抗冲击性能问题,采用Monte-Carlo方法创建了泡沫铝结构的二维细观模型,在常规态型近场动力学理论中引入了Mises屈服准则和线性各向同性强化模型,建立了近场动力学塑性本构的数值计算框架。基于近场动力学计算程序模拟了低速冲击作用下泡沫铝夹层结构的塑性变形以及有机玻璃背板的裂纹扩展形态,分析了泡沫铝芯材孔隙率对该夹层结构抗冲击性能和损伤模式的影响规律。结果表明：泡沫铝夹层结构良好的塑性变形能力是其发挥缓冲与防护作用的主要因素,并且在一定范围内,泡沫铝芯材孔隙率越高,则夹层结构具有更好的抗冲击性能;当泡沫铝孔隙率从0.4提升到0.7时,泡沫铝对冲击物的动能吸收率从90%提高到99%;模拟结果与实验结果具有较好的一致性,验证了模拟结果的准确性和分析结论的有效性。通过数值模拟,预测了有机玻璃背板的裂纹扩展形态,发现提高泡沫铝的孔隙率能获得更好的防护效果。     

Geometrical non-linear analysis of structures by finite elements

Meccanica - The paper shows a comprehensive analysis of geometrically non linear structural problems by the finite element method. The theoretical approach is based on a variational principle...     

Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour

An improved gradient-enhanced approach for softening elasto-plasticity is proposed, which in essence is fully nonlocal, i.e. an equivalent integral nonlocal format exists. The method utilises a nonlocal field variable in its constitutive framework, but in contrast to the integral models computes this nonlocal field with a gradient formulation. This formulation is considered ‘implicit’ in the sense that it strictly incorporates the higher-order gradients of the local field variable indirectly, unlike the common (explicit) gradient approaches. Furthermore, this implicit gradient formulation constitutes an additional partial differential equation (PDE) of the Helmholtz type, which is solved in a coupled fashion with the standard equilibrium condition. Such an approach is particularly advantageous since it combines the long-range interactions of an integral (nonlocal) model with the computational efficiency of a gradient formulation. Although these implicit gradient approaches have been successfully applied within damage mechanics, e.g. for quasi-brittle materials, the first attempts were deficient for plasticity. On the basis of a thorough comparison of the gradient-enhancements for plasticity and damage this paper rephrases the problem, which leads to a formulation that overcomes most reported problems. The two-dimensional finite element implementation for geometrically linear plain strain problems is presented. One- and two-dimensional numerical examples demonstrate the ability of this method to numerically model irreversible deformations, accompanied by the intense localisation of deformation and softening up to complete failure.     

Multi-scale modelling of strongly heterogeneous 3D composite structures using spatial Voronoi tessellation

3D composite materials are characterized by complex internal yarn architectures, leading to complex deformation and failure development mechanisms. Net-shaped preforms, which are originally periodic in nature, lose their periodicity when the fabric is draped, deformed on a tool, and consolidated to create geometrically complex composite components. As a result, the internal yarn architecture, which dominates the mechanical behaviour, becomes dependent on the structural geometry. Hence, predicting the mechanical behaviour of 3D composites requires an accurate representation of the yarn architecture within structural scale models. When applied to 3D composites, conventional finite element modelling techniques are limited to either homogenised properties at the structural scale, or the unit cell scale for a more detailed material property definition. Consequently, these models fail to capture the complex phenomena occurring across multiple length scales and their effects on a 3D composite’s mechanical response. Here a multi-scale modelling approach based on a 3D spatial Voronoi tessellation is proposed. The model creates an intermediate length scale suitable for homogenisation to deal with the non-periodic nature of the final material. Information is passed between the different length scales to allow for the effect of the structural geometry to be taken into account on the smaller scales. The stiffness and surface strain predictions from the proposed model have been found to be in good agreement with experimental results.The proposed modelling framework has been used to gain important insight into the behaviour of this category of materials. It has been observed that the strain and stress distributions are strongly dependent on the internal yarn architecture and consequently on the final component geometry. Even for simple coupon tests, the internal architecture and geometric effects dominate the mechanical response. Consequently, the behaviour of 3D woven composites should be considered to be a structure specific response rather than generic homogenised material properties.     

On the mechanical modelling of masonry structures using the F.E. technique

A non-linear finite element for the mechanical modelling of masonry structures is presented. Both material and geometrical non-linearities are introduced, developing the expression of the potential strain energy through appropriate average functions. The characteristics of the numerical model are explained and the approximations introduced in the analysis are discussed.

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Sommario Viene sviluppata la formulazione di un nuovo elemento finito per la modellazione meccanica di strutture murarie in campo non lineare. Vengono prese in esame sia non-linearita' geometriche che materiali, sviluppando l'espressione dell'energia potenziale elastica del solido murario attraverso l'introduzione di opportune funzioni medie sulle deformazioni. Vengono discusse le caratteristiche del modello numerico e le approssimazioni introdotte nell'analisi.

     

The implicit standard material theory for modelling the nonassociative behaviour of metals

Summary  Modelling the elastoplastic or elastoviscoplastic behaviour of metallic materials exhibiting strain hardening and damage leads to complex nonassociative constitutive equations, sources of many theoretical and numerical troubles. The usual modelling of a nonassociative constitutive equation leads to the loss of the interesting and very useful properties of generalised standard materials deriving from the key concepts of convexity and normality. The argument that will be developed is that the bipotential concept is an appropriate answer. In the first part, after introducing the state variables generally used to describe the behaviour of metallic materials, the constitutive equations subjected to the principles of thermodynamics are derived from two potentials. The state potential gives the state laws, and the bipotential of dissipation delivers the evolution laws for state variables, through the implicit normality assumption. The second part is devoted to several particular applications to metal elastoplasticity and elastoviscoplasticity models. Received 29 March 2000; accepted for publication 26 September 2000     

Fluid–structure interaction modelling of nonlinear aeroelastic structures using the finite element corotational theory

The application of the finite element corotational theory to model geometric nonlinear structures within a fluid–structure interaction procedure is proposed. A dynamic corotational approximately-energy-conserving algorithm is used to solve the nonlinear structural response and it is shown that this algorithm's application with a four-node flat finite element is more stable than the nonlinear implicit Newmark method. This structural dynamic algorithm is coupled with the unsteady vortex-ring method using a staggered technique. These procedures were used to obtain aeroelastic results of a nonlinear plate-type wing subjected to low speed airflow. It is shown that stable and accurate numerical solutions are obtained using the proposed fluid–structure interaction algorithm. Furthermore, it is illustrated that geometric nonlinearities lead to limit cycle oscillations.     

Microstructure-based modelling of multiphase materials and complex structures

Micromechanical approaches are frequently employed to monitor local and global field quantities and their evolution under varying mechanical and/or thermal loading scenarios. In this contribution, an overview on important methods is given that are currently used to gain insight into the deformational and failure behaviour of multiphase materials and complex structures. First, techniques to represent material microstructures are reviewed. It is common to either digitise images of real microstructures or generate virtual 2D or 3D microstructures using automated procedures (e.g. Voronoï tessellation) for grain generation and colouring algorithms for phase assignment. While the former method allows to capture exactly all features of the microstructure at hand with respect to its morphological and topological features, the latter method opens up the possibility for parametric studies with respect to the influence of individual microstructure features on the local and global stress and strain response. Several applications of these approaches are presented, comprising low and high strain behaviour of multiphase steels, failure and fracture behaviour of multiphase materials and the evolution of surface roughening of the aluminium top metallisation of semiconductor devices.     

On the modelling of dynamic structures with discontinuities

A method of simulation is developed for studying the dynamics of the structures with discontinuities using Matlab–Simulink. The concept of dynamic compliance is used for modeling the continuous elements of the structure and the local discontinuity is modeled as nonlinear feedback. As an example, a one-dimensional model of cracked bar under harmonic loading is considered for the simulation purpose.     

Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures

A repetitive pin-jointed, pre-twisted structure is analysed using a state variable transfer matrix technique. Within a global coordinate system the transfer matrix is periodic, but introduction of a local coordinate system rotating with nodal cross-sections results in an autonomous transfer matrix for this Floquet system. Eigenanalysis reveals four real unity eigenvalues, indicating tension–torsion coupling, and equivalent continuum properties such as Poisson’s ratio, cross-sectional area, torsion constant and the tension–torsion coupling coefficient are determined. A variety of real and complex near diagonal Jordan decompositions are possible for the multiple (eight) complex unity eigenvalues and these are discussed in some detail. Analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment, together with shear deformation in the perpendicular plane, but no bending–bending coupling; the choice of a structure having an equilateral triangular cross-section is thought responsible for this unexpected behaviour, as the equivalent continuum second moments of area are equal about all cross-sectional axes. In addition, an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling, and possible causes are discussed.     

Geometrical properties of the vorticity vector derived using large-eddy simulation

In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor and negative subgrid-scale stress tensor -τ_ij, enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of , and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of -τ_ij is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of -τ_ij and are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of .     

Finite-macro-element for modelling thin structures with integrated piezoelectric sensor-actor-elements

A finite element technique is presented, which integrates the behaviour of circular sensor-actuator-elements within a macro-element. The macro-element is applied to the investigation of thin structures, if the excitation and the measurement of membrane vibrations are accomplished by piezoelectric actuators and sensors. The electromechanical equations are solved analytically within the macro-element, in order to avoid a spatial discretisation of the piezoelectric actuators. The numerical efficiency is obvious, since the discretisation of the structure becomes independent of the piezoelectric components.     

A new simple method of implicit time integration for dynamic problems of engineering structures

This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai’s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems. The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China (G2000048702, 2003CB716707), the National Science Fund for Distinguished Young Scholars (10025208), the National Natural Science Foundation of China (Key Program) (10532040), the Research Fund for Oversea Chinese (10228028). The English text was polished by Keren Wang.     

Semi‐implicit subgrid modelling of three‐dimensional free‐surface flows

In this paper, a semi‐implicit numerical model for two‐ and three‐dimensional free‐surface flows will be formulated in such a fashion as to intrinsically account for subgrid bathymetric details. It will be shown that with the proposed subgrid approach the model accuracy can be substantially improved without increasing the corresponding computational effort. Copyright © 2010 John Wiley & Sons, Ltd.