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The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.

The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.

Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.

A complete investigation of the stabilized formulation of the compressible problem is addressed.

The purpose of this study is to present a multi-scale analysis methodology for calculating the effective stiffnesses and the micro stresses of helically wound structures efficiently and accurately. The helically wound structure is widely applied in ocean and civil engineering as load-bearing structures with high flexibility, such as wire ropes, umbilical cables and flexible risers. Their structures are usually composed of a number of twisted subcomponents with relatively large slender ratio and have the one-dimensional periodic characteristic in the axial direction. As the huge difference between the axial length and the cross-section size of this type of structures, the finite element modeling and theoretical analysis based on some assumption are usually unavailable leading to the reduction of computability; even the optimization design becomes infeasible.

Based on the asymptotic homogenization theory, the one-dimensional periodic helically wound structure is equivalent to the one-dimensional homogeneous beam. A novel implementation of the homogenization is derived for the analysis of the effective mechanical properties of the helically wound structure, and the tensile, bending, torsional and coupling stiffness properties of the effective beam model are obtained. On this basis, a downscaling analysis formation for the micro-component stress in the one-dimensional periodic wound structure is constructed. The stress of micro-components in the specified geometry position of the helically wound structure is obtained basing on the asymptotic homogenization theory simultaneously.

By comparing with the result from finite element established accurately, the established multi-scale calculation method of the one-dimensional periodic helically wound structure is verified. The influence of size effects on the macro effective performance and the micro-component stress is discussed.

This paper will provide the theoretical basis for the efficient elastoplastic analysis of the helically wound structure, even the fatigue analysis. In addition, it is necessary to point out that the axial length of the helically wound structure in the general engineering problems that such as deep-sea risers and submarine cables.

The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.

In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).

The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.

This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.

The great magnitude differences between the integral tunnel and its structure details make it impossible to numerically model and analyze the global and local seismic behavior of large-scale shield tunnels using a unified spatial scale, even with the help of supercomputers. The paper aims to present a combined equivalent & multi-scale simulation method, by which the tunnel's major mechanical properties under seismic loads can be represented by the equivalent model, and the seismic responses of the interested details can be studied efficiently by the coupled multi-scale model.

The nominal orthotropic material constants of the equivalent tunnel model are inversely determined by fitting the modal characteristics of the equivalent model with the corresponding segmental lining model. The critical sections are selected by comprehensive analyzing of the integral compression/extension and bending loads in the equivalent lining under the seismic shaking and the coupled multi-scale model containing the details of interest is solved by the mixed time explicit integration algorithm.

The combined equivalent & multi-scale simulation method is an effective and efficient way for seismic analyses of large-scale tunnels. The response of each flexible joint is related to its polar location on the lining ring, and the mixed time integration method can speed-up the calculation process for hybrid FE model with great differences in element sizes.

The orthotropic equivalent assumption is, to the best of the authors’ knowledge, for the first time, used in the 3D simulation of the shield tunnel lining, representing the rigidity discrepancies caused by the structural property.

Hybrid simulation, which is a general technique for obtaining the seismic response of an entire structure, is an improvement of the traditional seismic test technique. In order to improve the analysis accuracy of the numerical substructure in hybrid simulation, the purpose of this paper is to propose an innovative hybrid simulation technique. The technique combines the multi-scale finite element (MFE) analysis method and hybrid simulation method with the objective of achieving the balance between the accuracy and efficiency for the numerical substructure simulation.

To achieve this goal, a hybrid simulation system is established based on the MTS servo control system to develop a hybrid analysis model using an MFE model. Moreover, in order to verify the efficiency of the technique, the hybrid simulation of a three-storey benchmark structure is conducted. In this simulation, a ductile column—represented by a half-scale scale specimen—is selected as the experimental element, meanwhile the rest of the frame is modelled as microscopic and macroscopic elements in the Abaqus software simultaneously. Finally, to demonstrate the stability and accuracy of the proposed technique, the seismic response of the target structure obtained via hybrid simulation using the MFE model is compared with that of the numerical simulation.

First, the use of the hybrid simulation with the MFE model yields results similar to those obtained by the fine finite element (FE) model using solid elements without adding excessive computing burden, thus advancing the application of the hybrid simulation in large complex structures. Moreover, the proposed hybrid simulation is found to be more versatile in structural seismic analysis than other techniques. Second, the hybrid simulation system developed in this paper can perform hybrid simulation with the MFE model as well as handle the integration and coupling of the experimental elements with the numerical substructure, which consists of the macro- and micro-level elements. Third, conducting the hybrid simulation by applying earthquake motion to simulate seismic structural behaviour is feasible by using Abaqus to model the numerical substructure and harmonise the boundary connections between three different scale elements.

In terms of the implementation of the hybrid simulation with the MFE model, this work is helpful to advance the hybrid simulation method in the structural experiment field. Nevertheless, there is still a need to refine and enhance the current technique, especially when the hybrid simulation is used in real complex engineering structures, having numerous micro-level elements. A large number of these elements may render the relevant hybrid simulations unattainable because the time consumed in the numeral calculations can become excessive, making the testing of the loading system almost difficult to run smoothly.

The MFE model is implemented in hybrid simulation, enabling to overcome the problems related to the testing accuracy caused by the numerical substructure simplifications using only macro-level elements.

This paper is the first to recognise the advantage of the MFE analysis method in hybrid simulation and propose an innovative hybrid simulation technique, combining the MFE analysis method with hybrid simulation method to strike a delicate balance between the accuracy and efficiency of the numerical substructure simulation in hybrid simulation. With the help of the coordinated analysis of FEs at different scales, not only the accuracy and reliability of the overall seismic analysis of the structure is improved, but the computational cost can be restrained to ensure the efficiency of hybrid simulation.

The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.

The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time.

The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems.

For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications

Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.

Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.

The present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.

Provides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.

This paper aims to present a domain decomposition method to overcome the challenges posed by multi-domain, multi-scale high frequency problems.

A hybrid finite element and boundary integral procedure is also presented that allows for domains to employ different solution methods in different subdomains.

By decomposing large electromagnetic regions into smaller domains, the finite element method can cope with the simulation of electrically large problems.

Real life examples demonstrate the accuracy and efficiency of the new method.

The Robin transmission condition (RTC) is applied to link the domains and preserve field continuity on interfaces.

The purpose of this study is to enable performing reliability-based design optimisation (RBDO) for a composite component while accounting for several multi-scale uncertainties using a large representative volume element (LRVE). This is achieved using an efficient finite element analysis (FEA)-based multi-scale reliability framework and sequential optimisation strategy.

An efficient FEA-based multi-scale reliability framework used in this study is extended and combined with a proposed sequential optimisation strategy to produce an efficient, flexible and accurate RBDO framework for fibre-reinforced composite laminate components. The proposed RBDO strategy is demonstrated by finding the optimum design solution for a composite component under the effect of multi-scale uncertainties while meeting a specific stiffness reliability requirement. Performing this using the double-loop approach is computationally expensive because of the number of uncertainties and function evaluations required to assess the reliability. Thus, a sequential optimisation concept is proposed, which starts by finding a deterministic optimum solution, then assesses the reliability and shifts the constraint limit to a safer region. This is repeated until the desired level of reliability is reached. This is followed by a final probabilistic optimisation to reduce the mass further and meet the desired level of stiffness reliability. In addition, the proposed framework uses several surrogate models to replace expensive FE function evaluations during optimisation and reliability analysis. The numerical example is also used to investigate the effect of using different sizes of LRVEs, compared with a single RVE. In future work, other problem-dependent surrogates such as Kriging will be used to allow predicting lower probability of failures with high accuracy.

The integration of the developed multi-scale reliability framework with the sequential RBDO optimisation strategy is proven computationally feasible, and it is shown that the use of LRVEs leads to less conservative designs compared with the use of single RVE, i.e. up to 3.5% weight reduction in the case of the 1 × 1 RVE optimised component. This is because the LRVE provides a representation of the spatial variability of uncertainties in a composite material while capturing a wider range of uncertainties at each iteration.

Fibre-reinforced composite laminate components designed using reliability and optimisation have been investigated before. Still, they have not previously been combined in a comprehensive multi-scale RBDO. Therefore, this study combines the probabilistic framework with an optimisation strategy to perform multi-scale RBDO and demonstrates its feasibility and efficiency for an fibre reinforced polymer component design.

The purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.

In a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

An overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.

The uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.