Benchmarking Examples Research Articles

Finite element implementation of a seepage-stress coupling method for solid-liquid-gas three phases in porous media considering compressible gas

Some existing coupling models of porous media ignore the gas phase or gas compressibility, making them inadequate in describing the gas transport process and their effects on water infiltration and solid deformation. However, consideration of gas compressibility becomes crucial when involving the confined gas. Furthermore, the unsteady seepage free surface problem may make the numerical solution of seepage-stress coupling more complicated and difficult. To overcome the above problems, a new coupled seepage-stress method considering compressible gas is proposed. Based on the momentum balance equation of solid–liquid–gas, the three-phase model is constructed by making the pore liquid and compressible gas both satisfy the fluid equilibrium equation and continuity equation. Integration of the interface-correction level set method in the solid–liquid–gas three phases model provides a good solution for representing liquid–gas two-phase flow and solid deformation while describing the unsteady free surface between saturated and unsaturated zones. The primary variables in this model are solid displacement and liquid/gas pressure and its governing equations are discretized by finite element strategy. After comprehensively explaining the mathematical framework and numerical implementation, the reliability and effectiveness of the proposed method are validated through several benchmarking examples.

Multiscale modeling of laminated thin-shell structures with Direct FE[formula omitted

Shell finite element is computationally efficient and thereby favored in large-scale structural analysis. With the application of advanced materials, understanding the relation between micro-heterogeneities and structural behavior is important. To this end, we propose a multiscale method in the current contribution for modeling thin-walled fiber reinforced composite laminates with Mindlin–Reissner shell theory and Direct FE2. By exploiting the length scales in layered structure together with a shell formulation degenerated from continuum solid element, both in-plane and through-thickness periodicity can be assumed. A single-fiber unit cell attached to each Gauss point is employed as a representative volume element (RVE) rather than a through-thickness microstructure. In this way, the scale transitions are naturally dealt with using a first-order homogenization framework, in which the downscaling of transverse shear strain, commonly troublesome for the through-thickness RVE, is straightforward. The other merit inherited from Direct FE2 is that the two-scale problem is formulated in a single finite element analysis wherein the macro and micro DOFs are coupled based on the downscaling kinematics. It avoids the upscaling of the macroscopic stresses and tangents in the conventional nested FE2 scheme, which is challenging in the case of complex microstructural response. The developed method is then verified through several benchmarking examples, including a flat plate and two curve shells. Isotropic materials and composite laminates with homogeneous and heterogeneous RVEs have been examined. Two examples with plasticity and cohesive cracks are further presented to showcase its potential in modeling damage propagation in composite structures.

A local to global (L2G) finite element method for efficient and robust analysis of arbitrary cracking in 2D solids

This paper presents and validates a new local to global (L2G) FEM approach that can analyze multiple, interactive fracture processes in 2D solids with improved numerical efficiency and robustness. The method features: 1) forming local problems for individual and interactive cracks; and 2) parallel solving local problems and returning local solutions as part of the trial solution for global iteration. It has been demonstrated analytically (through a simple 1D problem) and numerically (through several benchmarking examples) that, the proposed method can substantially improve the robustness of the global solution process and significantly reduce the costly global iteration for convergence. The demonstrated improvement in numerical efficiency is up to 20∼40% for mildly unstable problems. For problems with severely unstable crack initiation and propagation, the improvement can be more significant. This new method is readily applicable to other popular methods such as the extended FEM (X-FEM), Augmented FEM (A-FEM) and Phantom-node method (PNM).

Effective thermo-viscoelastic behavior of short fiber reinforced thermo-rheologically simple polymers: An application to high temperature fiber reinforced additive manufacturing

This paper presents a procedure for the estimation of the effective thermo-viscoelastic behavior in fiber-reinforced polymer filaments used in high temperature fiber-reinforced additive manufacturing (HT-FRAM). The filament is an amorphous polymer matrix (PEI) reinforced with elastic short glass fibers treated as a single polymer composite (SPC) holding the assumption of thermo-rheologically simple matrix. Effective thermo-viscoelastic behavior is obtained by implementing mean-field homogenization schemes through the extension of the correspondence principle to continuous variations of temperature by using the time–temperature superposition principle and the internal time technique. The state of the fibers in the composite is described through the use of probability distribution functions. Explicit forms of the effective properties are obtained from an identification step, ensuring the same mathematical structure as the matrix behavior. The benchmark simulations are predictions of residual stress resulting from the cooling of the representative elementary volumes (REVs) characterizing the composite filament. The computation of the averaged stress in the benchmarking examples is achieved by solving numerically the stress–strain problem via the internal variables’ framework. Reference solutions are obtained from Fast Fourier Transform based full-field homogenization simulations. A comparative analysis is performed, showing the reliability of the proposed homogenization procedure to predict residual stress against extensive computations of the macroscopic behavior of a given microstructure.

A Novel Efficacious PID Controller for Processes With Inverse Response and Time Delay

Design of controller for the inverse response processes has been a challenge for researchers. Water level control in a steam boiler is one of the best examples, where the time delay and inverse response are inherent. Proportional Integral Derivative(PID) controller is the extensively employed regulator in industries. The present work introduces a new form of PID for the processes which are having time delay and inverse response simultaneously. The proposed PID is associated with a higher order filter. The controller and filter parameters are computed by using polynomial approach. Maximum sensitivity of the control loop is used to determine the tuning parameter. A set-point filter is utilized to diminish the settling time and overshoot in servo response. The suggested method is evaluated by considering several performance indices and bench marking examples. The proposed method is evaluated against the existing methods and tested in real-time scenario also.

A General Block Stability Analysis Algorithm for Arbitrary Block Shapes

In rock engineering, block theory is a fundamental theory that aims to analyze the finiteness, removability, and mechanical stability of convex blocks under different engineering conditions. In practice, the possible combinations of the fractures and joint sets that may generate key blocks can be identified by stereographic projection graphs of block theory. However, classic key block theory does not provide solutions for nonconvex blocks, which are very common in civil projects, such as those with underground edges, corners, and portals. To enhance the availability of block theory, a general algorithm that can analyze the removability and stability of blocks of arbitrary shapes is proposed in this paper. In the proposed algorithm, the joint pyramid for blocks of arbitrary shapes can be computed, and the faces of the blocks are grouped according to their normal vectors such that parallel or nonadjacent sliding faces with the same normal vector can be immediately identified when the sliding mode is determined. With this algorithm, blocks of arbitrary shapes can be analyzed, and users do not need to have experience interpreting graphs of block theory to take advantage of its accuracy and effectiveness. The proposed algorithm was verified by several benchmarking examples, and it was further applied to investigate the stability of the left bank rock slope of a dam. The results showed that the proposed algorithm is correct, effective, and feasible for use in the design and support of excavation in complex rock masses.

An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures

This work presents a Fluid–Structure Interaction framework for the robust and efficient simulation of strongly coupled problems involving arbitrary large displacements and rotations. We focus on the application of the proposed tool to lightweight membrane-like structures. Nonetheless, all the techniques we present in this work can be applied to both volumetric and volumeless bodies. To achieve this, we rely on the use of embedded mesh methods in the fluid solver to conveniently handle the extremely large deflections and eventual topology changes of the structure. The coupling between the embedded fluid and mechanical solvers is based on an interface residual black-box strategy. We validate our proposal by solving reference benchmarking examples that consider both volumetric and volumeless geometries. Whenever it is possible, we also compare the embedded solution with the one obtained with our reference body fitted solver. Finally we present a real-life application of the presented embedded Fluid–Structure Interaction solver.

Robustly Complete Synthesis of Memoryless Controllers for Nonlinear Systems With Reach-and-Stay Specifications

This paper proposes a finitely terminating algorithm to solve reach-and-stay control problems for nonlinear systems. The algorithm is guaranteed to return a control strategy if the specification is robustly realizable. Such a feature is desirable as the commonly used abstraction-based methods are sound but not complete for systems that are not incrementally stable. Fundamental to the proposed method is a fixed-point characterization of the winning set of the system with respect to a given specification, i.e., the initial states that can be controlled to satisfy the specification. The use of an adaptive partitioning scheme not only guarantees the approximation precision of the winning set but also reduces computational time. The effectiveness and efficiency are illustrated by several benchmarking examples.

Measuring precise fusion cross sections using an 8T superconducting solenoid

A novel fusion-evaporation residue separator based on a gas-filled superconducting solenoid has been developed at the Australian National University. Though the transmission efficiency of the solenoid is very high, precision cross sections measurements require this efficiency to be accurately known and vitally, requires knowledge of the angular distribution of the evaporation residues. We have developed a method to deduce the angular distribution of the evaporation residues from the laboratory-frame velocity distribution of the evaporation residues transmitted by the solenoid. The method will be discussed, focusing on benchmarking examples for 34S+89Y, where the angular distributions have been independently measured using a velocity filter (A. Mukherjee et al., Phys. Rev. C. 66, 034607 (2002)) . The establishment of this method now allows the novel solenoidal separator to be used to obtain reliable, precise fusion cross-sections.

A Conforming Augmented Finite Element Method for Modeling Arbitrary Cracking in Solids

Abstract This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method.

Modified predictor‐corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

SummaryThe high computational costs associated with the implicit formulation of discontinuous deformation analysis (DDA) have been one of the major obstacles for its implementation to engineering problems involving jointed rock masses with large numbers of blocks. In this paper, the Newmark‐based predictor‐corrector solution (NPC) approach was modified to improve the performance of the original DDA solution module in modeling discontinuous problems. The equation of motion for a discrete block system is first established with emphasis on the consideration of contact constraints. A family of modified Newmark‐based predictor‐corrector integration (MNPC) scheme is then proposed and implemented into a unified analysis framework. Comparisons are made between the proposed approach and the widely used constant acceleration (CA) integration approach and central difference (CD) approach, regarding the stability and numerical damping features for a single‐degree‐of‐freedom model, where the implications of the proposed approach on open‐close iteration are also discussed. The validity of the proposed approach is verified by several benchmarking examples, and it is then applied to two typical problems with different numbers of blocks. The results show that the original CA approach in DDA is efficient for the simulation of quasi‐static deformation of jointed rock masses, while the proposed MNPC approach leads to improved computational efficiency for dynamic analysis of large‐scale jointed rock masses. The MNPC approach therefore provides an additional option for efficient DDA of jointed rock masses.

A New Control Scheme for Integrating Processes with Inverse Response and Time Delay

Abstract This paper presents a novel technique in designing controller for integrating process with inverse response and time delay. Using Pade’s approximation, the positive zero is approximated to a negative zero by modifying the time delay of process. The polynomial approach is employed for the rearranged process to derive the controller parameters. The tuning parameter is selected based on the value of maximum sensitivity. Set point filtering is employed to reduce the overshoot in servo response. Various bench marking examples are considered to evaluate the proposed method. The evaluation is carried out in terms of various performances.

Zhang Neural Dynamics Approximated by Backward Difference Rules in Form of Time-Delay Differential Equation

Time-varying matrix inversion (TVMI) and tracking control of vehicular inverted pendulum (VIP) system are usually considered as two important benchmarking examples in mathematical science and control fields. In this paper, Zhang neural dynamics (ZND) method is used for solving these two problems. Besides, in order to investigate the effect of time delay (especially the time delay caused by the derivative approximation) on the ZND method when solving the above-mentioned two problems, backward difference rules in the form of time-delay differential equation are elegantly applied to approximating the ZND method, which is simply termed time-delay ZND method. Moreover, two theorems about time-delay ZND method are presented together with theoretical proofs. Finally, simulative tests of TVMI and tracking control of VIP system are conducted to show the effectiveness and accuracy of non-time-delay and time-delay ZND methods.

A Lagrangian gradient smoothing method for solid‐flow problems using simplicial mesh

SummaryA novel Lagrangian gradient smoothing method (L‐GSM) is developed to solve “solid‐flow” (flow media with material strength) problems governed by Lagrangian form of Navier‐Stokes equations. It is a particle‐like method, similar to the smoothed particle hydrodynamics (SPH) method but without the so‐called tensile instability that exists in the SPH since its birth. The L‐GSM uses gradient smoothing technique to approximate the gradient of the field variables, based on the standard GSM that was found working well with Euler grids for general fluids. The Delaunay triangulation algorithm is adopted to update the connectivity of the particles, so that supporting neighboring particles can be determined for accurate gradient approximations. Special techniques are also devised for treatments of 3 types of boundaries: no‐slip solid boundary, free‐surface boundary, and periodical boundary. An advanced GSM operation for better consistency condition is then developed. Tensile stability condition of L‐GSM is investigated through the von Neumann stability analysis as well as numerical tests. The proposed L‐GSM is validated by using benchmarking examples of incompressible flows, including the Couette flow, Poiseuille flow, and 2D shear‐driven cavity. It is then applied to solve a practical problem of solid flows: the natural failure process of soil and the resultant soil flows. The numerical results are compared with theoretical solutions, experimental data, and other numerical results by SPH and FDM to evaluate further L‐GSM performance. It shows that the L‐GSM scheme can give a very accurate result for all these examples. Both the theoretical analysis and the numerical testing results demonstrate that the proposed L‐GSM approach restores first‐order accuracy unconditionally and does not suffer from the tensile instability. It is also shown that the L‐GSM is much more computational efficient compared with SPH, especially when a large number of particles are employed in simulation.

Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification

This paper describes a new technique for identifying potentially parallelisable code structures in functional programs. Higher-order functions enable simple and easily understood abstractions that can be used to implement a variety of common recursion schemes, such as maps and folds over traversable data structures. Many of these recursion schemes have natural parallel implementations in the form of algorithmic skeletons. This paper presents a technique that detects instances of potentially parallelisable recursion schemes in Haskell 98 functions. Unusually, we exploit anti-unification to expose these recursion schemes from source-level definitions whose structures match a recursion scheme, but which are not necessarily written directly in terms of maps, folds, etc. This allows us to automatically introduce parallelism, without requiring the programmer to structure their code a priori in terms of specific higher-order functions. We have implemented our approach in the Haskell refactoring tool, HaRe, and demonstrated its use on a range of common benchmarking examples. Using our technique, we show that recursion schemes can be easily detected, that parallel implementations can be easily introduced, and that we can achieve real parallel speedups (up to 23.79× the sequential performance on 28 physical cores, or 32.93× the sequential performance with hyper-threading enabled).

Maximum Sensitivity Based New PID Controller Tuning for Integrating Systems Using Polynomial Method

Abstract This paper presents a new control methodology for a class of integrating systems. A PID controller augmented with a first order lead/lag filter is proposed for improved response. The polynomial approach is employed to derive the controller parameters. The novelty of the proposed method lies in the selection of pole locations. Multiple pole locations are considered where one of the poles is placed for cancelling the zero introduced by controller. The selection of tuning parameter is based on maximum sensitivity (MS). Set point weighting is employed to reduce the overshoot and settling time in the servo response. Various bench marking examples are adopted to evaluate the proposed method in terms of various performance indices. The results are superior to the recently proposed works in terms of both set point tracking and disturbance rejection.

Challenge problems for the benchmarking of micromechanics analysis: Level I initial results

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org .

Beam-machine Interaction at the CERN LHC

The radiation field generated by a high energy and intensity accelerator is of concern in terms of element functionality threat, component damage, electronics reliability, and material activation, but also provides signatures that allow actual operating conditions to be monitored. The shower initiated by an energetic hadron involves many different physical processes, down to slow neutron interactions and fragment de-excitation, which need to be accurately described for design purposes and to interpret operation events. The experience with the transport and interaction Monte Carlo code FLUKA at the Large Hadron Collider (LHC), operating at CERN with 4 TeV proton beams (and equivalent magnetic rigidity Pb beams) and approaching nominal luminosity and energy, is presented. Design, operation and upgrade challenges are reviewed in the context of beam-machine interaction account and relevant benchmarking examples based on radiation monitor measurements are shown.

Hadron production simulation by FLUKA

For the purposes of accelerator based neutrino experiments, the simulation of parent hadron production plays a key role. In this paper a quick overview of the main ingredients of the PEANUT event generator implemented in the FLUKA Monte Carlo code is given, together with some benchmarking examples.

Combining high productivity and high performance in image processing using Single Assignment C on multi-core CPUs and many-core GPUs

We address the challenge of parallelization development of industrial high-performance inspection systems comparing a conventional parallelization approach versus an auto-parallelized technique. Therefore, we introduce the functional array processing language Single Assignment C (SAC), which relies on a hardware virtualization concept for automated, parallel machine code generation for multi-core CPUs and GPUs. Additional software engineering aspects like programmability, productivity, understandability, maintainability, and resulting achieved gain in performance are discussed from the point of view of a developer. With several illustrative benchmarking examples from the field of image processing and machine learning, the relationship between runtime performance and efficiency of development is analyzed.