Efficient Numerical Model Research Articles

Generalized finite difference method for three-dimensional eigenproblems of Helmholtz equation

In this paper, a meshless numerical procedure, based on the generalized finite difference method (GFDM) is proposed to efficiently and accurately solve the three-dimensional eigenproblems of the Helmholtz equation. The eigenvalues and eigenvectors are very important to various engineering applications in three-dimensional acoustics, optics and electromagnetics, so it is essential to develop an efficient numerical model to analyze the three-dimensional eigenproblems in irregular domains. In the GFDM, the Taylor series and the moving-least squares method are used to derive the expressions at every node. By enforcing the satisfactions of governing equation at interior nodes and boundary conditions at boundary nodes, the resultant system of linear algebraic equations can be expressed as the eigenproblems of matrix and then the eigenvalues and eigenvectors can be efficiently acquired. In this paper, four numerical examples are provided to validate the accuracy and simplicity of the proposed numerical scheme. Furthermore, the numerical results are compared with analytical solutions and other numerical results to verify the merits of the proposed method.

Efficient numerical model for effective thermal conductivity of concrete with aggregates of different morphologies and imperfect interfaces

The existing numerical model for predicting the effective coefficient of thermal conductivity (CTC) of concrete usually ignores its mesostructure such as the three dimensional (3D) irregular aggregate morphology, imperfect interface, phase in voids, and spatial distribution of aggregates. Meanwhile, most numerical models adopt the uniform temperature gradient in the homogenisation process, resulting in the larger model size required for convergence and lower post-processing efficiency. An algorithm to generate concrete with aggregates of different morphologies and imperfect interfaces was proposed. Subsequently, a simple method of imposing the periodic boundary conditions and an efficient post-processing method were proposed, thereby reducing the time consumption in the numerical homogenisation substantially. In addition, based on the mesomechanical analytical model, DIGIMAT, and experimental data, the rationality of the proposed method and established models was validated, and the effect of the 3D mesostructure of concrete on its effective CTC was analysed. Results show that the concrete exhibits imperfect interfaces in its service life, especially in the dried working condition. The concrete gradation, phase in voids, and aggregate orientation have different degrees of influence on the effective CTC of concrete, and the effect of aggregate morphology can be ignored.

Simulation of runout behavior of submarine debris flows over regional natural terrain considering material softening

Evaluation of regional submarine debris flows is critical for quantitative assessment of vulnerable areas and reasonable design of geohazard mitigation measures. In this article, an efficient numerical model for kinematics of regional submarine debris flows is developed. The proposed model can simulate the runout process and morphological evolution of submarine debris flows over natural 3D terrain by solving 1D depth-averaged governing equations in a geographic information system (GIS). A strength softening equation is introduced to capture the degradation of sliding material strength during the runout process. The model is validated by a flume test, two slump tests, and a real case history of submarine debris flow (St Niklausen slide). Applications to Shenhu area, South China Sea, are presented to demonstrate the ability of the proposed model over complex natural terrain and the importance of considering material softening. Results show that the proposed model is capable of simulating the whole debris flow process and tracking the propagation of the sliding material. Simulation of submarine debris flow without material softening will underestimate the disaster consequences. In addition, the influences of the ambient fluid and the yield strength of the sliding material on its runout behavior are also discussed.

Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi–Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

Coupled thermo-hydro-mechanical-phase field modeling for fire-induced spalling in concrete

This paper aims at developing an efficient numerical model to numerically reproduce the fire-induced spalling process taking place in concrete and to investigate the underlying mechanism of thermal spalling. To deal with complex crack patterns and with ease of extending to multi-physics problem, phase field method is employed for crack modeling. The primary objective of this manuscript is to develop a coupled thermo-hydro-mechanical-phase field model and the numerical solution framework. The effects of length scale parameter, staggered solution methods, and related factors on mechanical fields, as well as the impact of fracture on mass transfer and heat conduction are investigated. It is concluded that spalling is a result of combined thermal expansion and vapor pressure, among which thermal effect plays a major role and vapor pressure accelerates the occurrence of spalling.

Method for considering corroded joints in buckling analysis of single-layer reticulated shell structures

In this paper, an efficient numerical algorithm for considering the corroded joints is originally proposed. This method is utilized to estimate the buckling factor of single-layer reticulated shell structures (SLRSS) connected by welded hollow spherical joints (WHSJs) which is commonly used in reticulated shell structures. WHSJs in actual projects are subjected to corrosion with various severities since they have been utilized 50 years ago. The existing literature mainly focused on the mechanical behavior of WHSJs, and the influence of corroded WHSJs on structural buckling capacity is seldom studied due to the lack of efficient numerical algorithm. In the present study, a numerical method considering the degradation of connection is proposed to investigate the buckling capacity of single-layer reticulated shell. The randomness of bending (axial) stiffness is achieved by double element. The influences of bending and axial stiffness and their capacities are revealed. A probabilistic distribution model of buckling capacity is proposed by performing stochastic numerical analysis. The main contribution of this work is proposing the efficient numerical model for considering degraded connection. The conclusions derived in this study can provide reference for the safety estimation of SLRSS.

Modeling variable-density flow in saturated-unsaturated porous media: An advanced numerical model

Modeling variable-density flow in unconfined aquifers is a challenging task because of the nonlinear coupling between variably saturated flow and contaminant transport. This results in a highly nonlinear system since the strongly nonlinear Richards flow equation is, in addition, coupled to the advection-dispersion transport equation by viscosity and density variation. The solution of such a nonlinear system is often subject to convergence issues and can be very expansive in terms of computational time, especially for large-scale problems. Conventional numerical algorithms based on the sequential approach and the classical finite difference or finite element methods with the first-order backward Euler time integration scheme are generally inefficient and/or do not provide satisfactory results. In this work, we develop a new efficient and accurate 2D numerical model for the transport of dense contaminants in unsaturated porous media that allows for the simulation of large-scale problems. This research describes a new model that combines advanced spatial discretization methods (mixed hybrid finite element method, discontinuous Galerkin finite element method, and multipoint flux approximation method) with higher-order time integration techniques via the method of lines (MOL). The latter allows one to adapt the time step's size and the order of the time integration to improve the computational efficiency while maintaining accuracy. The robustness and accuracy of the new model are shown by comparison against a widely used commercial code based on the standard finite element method. The applicability of the developed model to a large-scale problem is then investigated by simulating saltwater intrusion under a climate change projection and long-term pumping regimes for the Akkar coastal aquifer in Lebanon using a simplified 2D conceptual model.

Rapid thermalization by adaptive flow reorientation

Aim of this paper is the enhancement of scalar transport (heat, chemical species) in flow systems with reorientations of a laminar base flow. Conventional heating/mixing protocols comprise of temporal or spatial periodic reorientations of these base flows to promote fluid mixing. However, thermal homogenisation rates of scalar fields are not necessarily accelerated with these approaches due to the substantial effect of diffusion and/or chemical reactions on heat/chemical transport. In the present study we numerically study heat transport with an adaptive approach for an entire parameter space of fluid and flow properties. Key to the approach is real-time control of the fluid flow based on the scalar field due to an efficient numerical model. Results show that the adaptive approach can significantly enhance heat transport over the conventional periodic heating/mixing approach designed for efficient mixing.

Large-Scale Welding Process Simulation by GPU Parallelized Computing

The computational design of industrially relevant welded structures is extremely time consuming due to coupled physics and high nonlinearity. Previously, most welding distortion and residual stress simulations have been limited to small coupons and reduced order (from three-dimensional [3D] to two-dimensional [2D]), or inherent strain approximations were used for large structures. In this current study, an explicit finite element code based on a graphics processing unit was utilized to perform 3D transient thermomechanical simulation of structural components during welding. Laser brazing of aluminum alloy panels as representative of automotive manufacturing scenarios was simulated to predict out-of-plane distortion under different clamping conditions. The predicted deformation pattern and magnitude were validated by laser scanning data of physical assemblies. In addition, the code was used to investigate residual stresses developed during multipass arc welding of a nuclear industry pressurizer surge nozzle and subsequent welding repair where a 3D simulation was necessary. Taking the experimental data as reference, the 3D model predicted better residual stress distribution than a typical 2D asymmetrical model. Stress evolution in welding repair was also presented and discussed in this study. The efficient numerical model made it feasible to use integrated computational welding engineering to simulate welding processes for large-scale structures.

Optimization of hybrid cable networks with dampers and cross-ties for vibration control via multi-objective genetic algorithm

For long-span cable-stayed bridges, interconnecting adjacent cables using cross-ties and connecting each cable to bridge deck become a promising solution for cable vibration mitigation, leading to hybrid cable networks. However, optimizing the system parameters and configuration for best vibration control effects is still challenging. Therefore, this study proposes an optimization method based on three important ingredients, i.e., a general and efficient numerical model of cable networks, a reasonable definition of the optimization objectives, and a multi-objective optimization method. The cable network is modeled using the component mode synthesis method with modal expansion and quasi-static correction, the optimization objectives consider both multi-mode damping effects and stiffness enhancement, and the multi-objective genetic algorithm is then employed. The proposed method is first verified by comparing with analytical methods when applying to relatively simple cable–damper systems. Subsequently, a five-cable network is studied using the method for optimal design of cross-tie and damper parameters. Furthermore, the method is applied to optimize cross-ties and dampers for the eight longest cables in the Sutong Bridge, considering different numbers, locations and anchoring conditions of the cross-ties. The results have demonstrated the effectiveness of the proposed method in dealing with real-world large-scale cable networks. It is shown that the optimization can ensure that vibrations in local modes of the cable network are dominated by cable segments with a damper installed in the span and hence are sufficiently damped. Besides, damping ratios of hybrid cable networks are shown to be sensitive to the cross-tie location and parameters while they are relatively insensitive to the damper coefficients.

Efficient mass conservative numerical model for solving variably saturated groundwater flow

A multi-dimensional mass conservative numerical method, particularly suitable for limited computational resources, is developed for solving transient variably saturated groundwater flow problems. The Richards equation is discretized spatially with a finite element method and temporally with an implicit Euler scheme, in which mass-conservative and mass-lumping techniques are used to keep the numerical simulation stable. In addition, the stiffness and mass matrices involved are approximated in a way to guarantee less computational effort. To confirm the accuracy and the efficiency of this code, we verified it using benchmark tests using one, two and three-dimensional problems. The present model is also applied to a real field case problem, where its superiority is clearly demonstrated. The code achieved reliable results for each problem.

Methodology for parameter identification on a thermoplastic composite crash absorber by the Sequential Response Surface Method and Efficient Global Optimization

Numerical simulations for crashworthiness require the definition of material properties that are not always predictable with standard experimental tests. This paper deals with the numerical optimization of a thermoplastic composite material model. The component is a vehicle impact attenuator made of an innovative All-PP (PolyPropylene) composite material. The peculiar failure mechanism of this material makes the numerical simulation of the collapse a difficult challenge to achieve with a trial and error calibration of the material card. Therefore, an optimization procedure is proposed to determine the material parameters. The optimization is implemented in LS-OPT, where the mean square error between the experimental and numerical load–displacement curves is the objective function to be minimized. Two test cases are considered: (1) optimization of the material card based on the full load–displacement curve from the experimental tests and (2) optimization of relevant parameters of a numerical trigger added to control initial contact instabilities between the impacting rigid wall and the component in the numerical simulations. The optimization strategies Sequential Response Surface Method (SRSM) and Efficient Global Optimization (EGO) are used. The results show that the presented methodology allows characterizing the studied composite material and thus obtaining a more efficient numerical model.

Advanced Structural Health Monitoring Method by Integrated Isogeometric Analysis and Distributed Fiber Optic Sensing.

Attempts in digital management of structures are among the most popular topics in the trend of Information of Things (IoT). However, the implementation lags behind. This work recognized that Computer Aided Design (CAD) comprises the core of modern engineering; thus, most digital information can be available if CAD is used not only in design but also for life cycle structural health monitoring (SHM). Based on this concept, the newly designed method utilizes the isogeometric analysis (IGA) tool to include the Distributed Fiber Optic Sensing (DFOS) information by proposing a fiber mesh model. The IGA model can be obtained directly from CAD, and the boundary conditions can be provided directly or indirectly from DFOS in real time and remotely. Hence a practical method of SHM is able to achieve highly efficient and accurate numerical model creation, which can even accommodate non-linear constitutive property of materials. The proposed method was applied to a pipe deformation model as an example. The inverse analysis method is also shown to determine the contact force for loading on the pipe, which shows the potential for many engineering applications.

An efficient RANS numerical model for cross-shore beach processes under erosive conditions

In this work, a new numerical model for cross-shore beach profile evolution, IH2VOF-SED, is developed. It consists in the bidirectional coupling of a 2D RANS hydrodynamic solver and a sediment transport module. The resulting model is extensively validated against three benchmark cases at different scales, attending to the hydrodynamics, bottom shear stress and bathymetry evolution. Comparisons between experimental and numerical results show a good agreement for both the flow variables and the seabed evolution in all the validation cases without making use of calibration parameters. Additionally, the qualitative analysis of the results is in accordance with previous experimental observations of sediment transport induced by breaking waves. The computational cost is greatly reduced to about 1/10 of other available RANS models. As a novel aspect regarding RANS models, the model is able to simulate the swash zone and changes in the position of the coastline. A good compromise between precision and computational cost is achieved, allowing for an in-depth analysis of the processes leading to the cross-shore profile evolution.

Efficient numerical model for progressive collapse analysis of prestressed concrete frame structures

Prestressed concrete (PC) frames are becoming an attractive solution for building structures due to the lightweight, aesthetics, and high resistance of their structural members. Nonetheless, few experimental and numerical studies have been carried out to investigate the progressive collapse resistance of PC frame structures, which is a key capacity feature to withstand extreme events. In this paper, a numerical model is proposed for progressive collapse analysis of PC beam-column sub-assemblages. The model was developed in OpenSees finite element software, simulating frame members via fiber beam-column elements, prestressing tendons (PTs) through corotational truss elements, the bond-slip behavior at the beam-column joint by zero-length elements, and coupling between the reinforced concrete beam and the PTs through kinematic compatibility conditions. The proposed modeling approach was validated through simulation of seven previously tested sub-assemblages under middle column removal. Numerical results indicate that the model allows a satisfactory simulation of vertical load–displacement pushdown curves, horizontal reaction–displacement curves, as well as local behaviors (e.g., rebar slip and fracture). Furthermore, a parametric study was conducted based on the validated numerical model to analyze the influence of effective prestress, tendon-concrete bond behavior, and tendon profile on the progressive collapse performance of PC sub-assemblages.

Thermal analysis on Darcy‐Forchheimer swirling Casson hybrid nanofluid flow inside parallel plates in parabolic trough solar collector: An application to solar aircraft

As a try, this work has been focused in the way towards the effective contribution in the field of solar aviation using renowned nanotechnology. After realizing the causes and effects of traditionally used energy forms, the search of cost-efficient, eco-friendly, and most prominent renewable source leads us back to the solar utilities. Research era of solar radiation-powered aircraft has been in trend. Focusing on that, an efficient numerical model representing the flow and thermal aspects of a parabolic trough surface collector (PTSC) embedded on solar aircraft wings has been adopted for this study. As the first time with the note, an eminent and leading form of thermal efficient fluid of kind, the Casson hybrid nanofluid has been engaged with the expectations of enhanced performance in the solar aircraft wings. To test it, a trending reputable numerical scheme of the Keller-box method has been utilized and the parametrical studies were carried out. The upshots of those studies provide the affable proofs in favor of our expectations towards the improved solar wings with better thermal efficiency. The glimpse of those successes in the parametrical level has been showcased in the forms of tables and graphs. The lateral “x” direction significant about the inertial forces, suspended particle ratio, and skin resistance phenomena, while for the transverse fluidity in the “y” direction were has to be concern about the magnetic interactions, rotational coordinates, viscous nature of the fluid along with the porous states. The power of hybrid nanofluid combos was exposed in higher notes in a unique state of solar aircraft wings. Furthermore, the thermal efficiency of hybrid nanofluids over nanofluids got down to a minimal level of 6.1% and peaked up to 21.8%.

On the tribo-dynamic interactions between piston skirt-liner system and pin assembly in a gasoline engine

Piston Skirt-Liner (PSL) system and Piston Pin Bearing (PPB), two key friction pairs in piston-assembly, interact with each other via impact and friction when transmitting the combustion load to crank train. Literature reporting such an interaction behavior in terms of tribology and dynamics is still rare, due to the complexity in a systematic modeling way. This paper proposed an efficient numerical model that fully couples these two friction pairs to investigate tribo-dynamic interactions between them. The model is built by coupling Reynolds-based mixed lubrication models for the friction pairs with Lagrange multibody motion equations for the piston-connecting rod-crank mechanism. Coupling effects between the piston skirt-liner system and the pin assembly are explored by comparing the cases contain the two friction pairs and one of them. Based on the above analyses, some design parameters including pin assembly clearance and pin offset, are further studied to disclose their influences on the tribo-dynamic performance of these two friction pairs. This work has a guiding significance for the systematic design of piston-assembly aiming to improve the dynamic property, economical efficiency and environmental-friendliness of engines.

Shape optimization of studs in double-leaf plasterboard walls for maximal broadband sound insulation and minimal material use

The cross-sectional shape of the metal studs in a double-leaf wall has a significant influence on its sound insulation. In a recent study, a numerical optimization of the stud shape resulted in designs that offer a significant increase in broadband airborne sound insulation, both when compared to conventional C-shaped studs and commercially available acoustic studs, but at the expense of a much higher material use. In the present work, a multi-objective optimization of the stud shape is aimed at, so as to find an optimized trade-off between the stud material cost and the sound insulation of the overall system across the entire building acoustics frequency range. This is achieved by combining a computationally efficient, iterative multi-objective optimization scheme with a computationally efficient numerical sound insulation prediction model of sufficient accuracy. Pareto fronts, which represent the set of optimal combinations of sound insulation and stud material use, are computed for a range of plasterboard wall systems that differ in cavity depth, number of sheets of plasterboard and stud type (symmetric or point-symmetric). For nearly all walls with symmetric studs, the Pareto fronts show that the introduction of a single deep indentation in the stud results in a high increase in sound insulation at a limited increase in material cost compared to simple C-shaped studs while two or three deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. For nearly all walls with point-symmetric studs, the Pareto fronts show that the introduction of two deep indentations results in a high increase in sound insulation at a limited increase in material cost compared to Z-shaped studs while four deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. It is shown that often, the acoustic performance of commercially available acoustic stud shapes can be further improved with less material used to produce the stud and sometimes even a shallower cavity.

An efficient numerical model for predicting residual stress and strain in parts manufactured by laser powder bed fusion

Computational modeling of additively manufactured structures plays an increasingly important role in product design and optimization. For laser powder bed fusion processes, the accurate modeling of stress and distortion requires large amount of computational cost due to very localized heat input and evolving complex geometries. The current study takes advantage of a graphics processing unit accelerated explicit finite element analysis code and approximated heat conduction analysis to predict the macroscopic thermo-mechanical behavior in laser selective melting. Adjacent layers and tracks were lumped to reduce the number of time steps and elements in the finite element model. The effects of track and layer grouping on prediction accuracy and solution efficiency are investigated to provide a guidance for a cost-effective simulation. Thin-wall builds from Inconel alloy 625 (IN625) powders were simulated by applying the developed modeling approach to get the detailed residual stress and distortion at a computational speed 50 times higher than conventional approach. Under repeated heating and cooling cycles, a high tensile stress was produced near surfaces of a build due to a larger shrinkage on surface than that in central area. It is also shown that horizontal stresses concentrate near the root and top layers of the IN625 build. The predicted residual elastic strain distribution was validated by the experimental measurement using x-ray synchrotron diffraction.

A novel 2-D equivalent numerical model of helix energy pile based on heat transfer characteristics of internal heat convection

Numerical modeling has been widely used to simulate the heat transfer of ground heat exchanger (GHE), However, there is a lack of analysis and comparison of different models and methods, for helix energy pile, there is a lack of an efficient and accurate numerical model to study the complex heat transfer problems. In this paper, taking a novel truncated cone helix energy pile (CoHEP) as the object, a two-dimensional(2-D) equivalent heat conduction model considering the heat transfer characteristics of the heat convection in the buried pipe was established, at the same time, a three-dimensional(3-D) full scale model and a 2-D ring coils model were established. By comparing the simulation results of three numerical models with the experimental results under the same conditions, the effects and suggestions of meshing on different models, the model characteristics and main error sources of different models were analyzed. The long-term and short-term simulation results and temperature distribution characteristics of different models were further analyzed. The study shows that the 3-D model has the highest accuracy in the simulation process, but the simulation efficiency is low, and it is easy to be affected by meshing. The 2-D ring coils model has high simulation efficiency, but the long-term simulation error is large, and the thermal influence radius of the pipe is smaller than the actual situation. For the 2-D equivalent model, the simulation error is small, and the thermal influence radius is close to those of the 3-D full scale model, and the effect of long-term simulation is obviously better than that of the 2-D ring coils model. The results indicate that the 2-D equivalent model effectively improves the simulation accuracy of the 2-D heat conduction numerical model, it can obtain the temperature distribution inside and outside the buried pipe which is closer to the actual situation with less calculation and higher simulation accuracy.