Mesh Size Requirements Research Articles

A novel elastic strain energy density approach for fatigue evaluation of welded components

The averaged elastic strain energy density (SED) within a characteristic volume radius R has been investigated and applied for characterizing the fatigue strength of welded joints for decades. However, engineering applications are still relatively rare. The main reason is that the calculation process is cumbersome due to fine mesh size and circular pattern requirements. This study proposes a novel approach of SED without requiring special finite element size and special layout requirements. First, a novel approach of the notch stress solution is presented. As a result, the present solution differs from the conventional approach which has been focused on notch tip singular stress field. Then, an averaged strain energy density can be obtained analytically by taking advantage of the new notch stress solutions presented in this study. Both the closed-form notch stress solutions and resulting expression for average strain energy density have been validated by FEA results. Subsequently, a large number of fatigue tests published in the literature are selected to examine the effectiveness of the evaluation approach of SED on interpreting fatigue behaviors of welded joints. Finally, a procedure for practical engineering application is established and verified by a group of fatigue tests of 3D gusset welded components.

Efficient sublaminate-scale impact damage modelling with higher-order elements in explicit integration

Damage modelling in composite structures with ply-level discretisation is computationally expensive for analysing large structures. In such cases homogenisation to the sublaminate length-scale is essential. However finite element discretisation requirements in bending problems imposed by conventional explicit-solver single-integration point solid elements results in a computationally expensive mesh, eroding the advantages of the larger length-scale. To benefit from using the sublaminate-scale and model the bending and torsional strains accurately a higher-order continuum solid element formulation is used in this work. This improved intra-element continuity enables evaluation of intralaminar strains and the corresponding damage at the sublaminate-scale accurately. Ply-level distributions are imposed through the thickness of these sublaminates to be able to use any ply-level damage initiation and evolution criteria available in the literature. Interlaminar damage calculation is performed using adaptively initiated higher-order cohesive segments thus simplifying pre-processing effort and enabling coarser in-plane mesh sizes without being limited by the mesh size requirements of cohesive zone modelling. This sublaminate-scale damage modelling strategy is verified using impact modelling examples performed with explicit time integration. Computational benefits are compared against conventional linear elements.

Numerical simulation of bluff body turbulent flows using hybrid RANS/LES turbulence models

Many engineering applications involve turbulent flows around bluff bodies. Because of their intrinsically unsteady dynamics, bluff body characteristic flows feature unique turbulence-related phenomena, which makes their numerical modeling challenging. Accordingly, accounting for a circular bluff body flow configuration, three different turbulence modeling approaches are investigated in this work, (i) Reynolds-averaged Navier–Stokes (RANS), (ii) large eddy simulation (LES), and (iii) hybrid RANS/LES. Regarding the hybrid approaches, two variants of the detached eddy simulation (DES) one, delayed DES (DDES) and improved delayed DES (IDDES), are studied. As RANS model, the $$\mathrm{k}-\mathrm{\omega SST}$$ is utilized here. This RANS model is also used as the background one for both DDES and IDDES. Wall-adaptive local eddy viscosity (WALE) is used in turn as the sub-grid scale (SGS) model for LES. The velocity two-point correlation function is used to assess the mesh size requirements. When compared to experimental data, the obtained numerical results indicate that RANS overestimates the recirculating bubble length by over 18% and is not capable of describing the turbulent kinetic energy and the flow anisotropy in agreement with the experimental data. In contrast, LES, DDES, and IDDES are all within 1% of the recirculating bubble length while predicting both the Reynolds stress tensor components and the corresponding flow anisotropy in agreement with the measurements. Besides, normalized anisotropy tensor invariants maxima in the shear layer were reproduced by all scale resolving models studied here, but they failed to yield the local extrema measured within the wake recirculation region. A comparative analysis of the anisotropic Reynolds stress tensor invariances underscores the adequacy of the scale resolving models.

Adaptive fourth-order phase-field modeling of ductile fracture using an isogeometric-meshfree approach

The fourth-order phase-field modeling of ductile fracture in elastic–plastic materials is performed via an adaptive isogeometric-meshfree approach. In the developed phase-field model, the total energy functional consists of the elastic contribution and the dissipated contribution because of fracture and plasticity. The coupling of the plasticity to fracture is implemented by a degradation function that is applied to the elastic energy. The present fourth-order phase-field model is capable of relaxing the mesh size requirements while accurately regularizing sharp cracks. To further enhance the computational efficiency, the isogeometric-meshfree approach is adopted for the numerical implementation of the phase-field model within a staggered computational framework. The developed approach can flexibly implement the C1-continuity of a crack phase field that is required by the fourth-order model. Moreover, an adaptive mesh refinement strategy is developed, which includes the gradient-based refinement indicators and the field transfer operators. Numerical simulations of a series of representative cases show that the developed fourth-order model can accurately and efficiently capture complex ductile fracture patterns including plastic localization, crack initiation, propagation, and merging, which demonstrates the reliability of the adaptive fourth-order phase-field modeling of ductile fracture.

Application of a BEM model with dipole elements

A potential flow code is extended to include dipole elements to handle potential flow problems for offshore structures consist of thin shell geometry with both sides exposed to ocean waves. The solution on dipole elements can be represented by the drop of fluid potential across the thin shell surface. By adjusting the porous effect parameter, such a dipole element model can be applied for the solid impervious thin shell structures, porous surfaces and even the imaginary sheets attached to the sharp edges where the local flow dissipation occurs. Special attention is paid on different approaches to evaluate the drift forces on floating bodies with porous surface, including the traditional far field and pressure integration methods as well as the control surface integration approach. The solutions from the BEM model on excitation forces, off-body kinematics and drift forces are verified against the analytical solutions for a concentric porous cylinder system fixed at the seabed. The numerical performance of a two-layer source/sink model with very small gaps is investigated, taking the results from the corresponding dipole element model as the baseline. It is suggested that the mesh size requirement from DNV-RP-C205 is too strict for the two-layer panel model in the case that the exact fluid velocity on both sides of the wall is not needed. The proposed model is demonstrated in two case studies which involve the internal fluid dynamics inside tanks with interior web frame structures of a floating barge for one case and the damping effects from the sharp edge of a box barge model for the other case.

Reproductive environment of the decreasing Indian river shad in Asian inland waters: disentangling the climate change and indiscriminative fishing threats.

The regional climate has significantly warmed with erratically declining annual rainfall and intensified downpour within a narrower span of monsoon months, which led to an increased trophic state (≈algae) in most inland waters. Freshwater clupeids vitally control the aquatic food chain by grazing on algae. Despite increasing food availability, IUCN Red List® revealed 16 freshwater clupeids with a decreasing population trend. We investigated one such species' reproductive dependencies, Gudusia chapra (Indian river shad), in the lower Gangetic drainage (India) under a mixed context of climate change and overfishing. Monthly rainfall (≥ 60-100 mm) and water temperature (≥ 31-32 °C) are key breeding cues for females. The regional climate seems inclined to fulfill these through the significant part of the breeding season, and indeed the species has maintained consistent breeding phenology over 20 years. Other breeding thresholds relevant to fishing include size at first maturity (≥ 6.8 cm; reduced by ~ 25-36%) and pre-spawning girth (Girthspawn50 ≥ 7 cm; first record). Girthspawn50 is a proxy of the minimum mesh size requirement of fishing nets to allow safe passage of "gravid" females (+ 22% bulged abdomen) and breed. The operational fishing nets (3-10 cm mesh) probably have been indulged in indiscriminative fishing of gravid females for generations. Under a favorably changing climate and food availability, existing evidence suggests a fishery-induced evolution in regional females (to circumvent such mesh sizes) through earlier maturation/puberty at smaller sizes. It could be an early warning sign of population collapse (smaller females → lessening fecundity → fewer offspring). Overfishing seemed to be a bigger threat than climate change.

Application of scaled boundary finite element method for vibration-based structural health monitoring of breathing cracks

The dynamic response of the host structure to a high-frequency actuation is usually used for the detection of tiny damage in structures in the form of breathing crack. The simulation of the microcrack’s effect on the response is essential for several damage identification targets. The conventional finite element method suffers from very small mesh size requirements to address the high-frequency problems, resulting in very large mass and stiffness matrices. In this study, the scaled boundary finite element method was applied to model different schemes of structural health monitoring of a structure with breathing cracks based on high-frequency vibration. The scaled boundary finite element method discretizes only the boundary of the model and thus substantially reduces the size of structural matrices. The node-to-node contact strategy was introduced to the scaled boundary finite element method to capture the contact problem that occurs during the vibration of the breathing crack. As breathing crack vibration results in some nonlinear effects, the simulation of three phenomena was of interest: higher harmonic generation, frequency shift, and vibro-acoustic modulation. A shooting method was used for efficient time integration and description of the frequency response function in the nonlinear regime. According to the results, the scaled boundary finite element method is of great power, efficiency, and accuracy to treat the contact problems, especially in high-frequency regimes. Moreover, the nonlinear methods provide certain advantages over the linear techniques in the early detection of incipient damage.

Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures

ABSTRACTThis contribution is addressing the ultimate limit state design of massive three‐dimensional reinforced concrete structures based on a finite‐element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state‐of‐the‐art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures.

An augmented cohesive element for coarse meshes in delamination analysis of composites

Numerical analysis of delamination failure in composite laminates is very often carried out with cohesive interface element in a finite element framework, due to their robustness and ease of use. Explicit time integration is often preferred, to overcome material and damage non-linearity and impact loading scenarios. However, a very fine mesh is needed to correctly represent the nonlinear cohesive zone ahead of the numerical crack tip to achieve a stable and mesh size insensitive global failure response. This is especially true for mode I delamination cases, where the cohesive zone is extremely small, owing to a low critical energy release rate. This mesh size requirement limits the applicability of cohesive zone models largely to coupon scale problems. The current work augments cohesive elements with additional rotational degrees of freedom at the nodes, which enables a higher order displacement approximation and allows relatively coarser mesh to be used. The present formulation is applied to a mode I delamination benchmark problem, which demonstrates the superiority of the augmented element over the traditional cohesive element in terms of coarse-mesh accuracy and computational time saving.

Status of fisheries law compliance in some fish landing sites in two local government areas of Rivers state, Nigeria

Illegal and overfishing are major threat to fisheries resource sustainability in Nigeria. The study determined social characteristics of fishers, level of awareness of the law and level of enforcement of fisheries law. A simple random sampling technique using 320 questionnaires was adopted to select the sampled population from four artisanal riverine communities along New Calabar River and Bonny Estuaries in Rivers State namely Station 1 (Nembe waterside), Station 2 (Mgbuosimini), Station 3 (Isaka-Bundu) and Station 4 (Borokiri-Rex-Lawson waterside). Respondents were identified through household listing. The level of education of fishers indicated that most of the sampled fishers were educated. From the respondents, only 1.56% was aware of the law. There was very high level of non-compliance to the 76 mm mesh size requirement; Nembe waterside, had 83.00%, Mgbuosimini had 76.00%, Isaka-Bundu had 80.00% and Borikiri Rex-Lawson Waterside had 85.00% mesh sizes less than 76 mm requirement. This indicated a violation of the mesh size requirement due to ignorance on the part of fishers and open access to the marine resources. Fishers agreed that the law should be reviewed. Therefore, the study recommends that there should be programmes to increase awareness of review of the provisions and enforcement of the law. Key Words : Factors, influencing, Fisheries Law, compliance, landing sites

An algorithm for decomposition of sub-domains and quadrilateral mesh generation with line constraints

The technique for quadrilateral mesh generation on arbitrary 2-D domain has been quite mature; however, the existing methods and software can not directly deal with mesh generation with internal line constraints. In flood analysis and other analysis, the analysis models often contain a large number of constraint lines. In mesh generation, the sides of elements besides constraint lines must be attached to constraint lines, so that boundary conditions can be defined on these constraint lines. In this paper, a general method for automatic quadrilateral mesh generation with internal line constraints is presented. The mesh generation process is mainly divided into two stages, i.e. the automatic decomposition of sub-domains and quadrilateral mesh generation in each sub-domain. The sub-domains enclosed by constraint lines and boundaries are determined automatically with the proposal algorithm in this paper. Then nodes are generated on each edge of sub-domains based on mesh size requirements. By solving an integer linear programming problem, the number of nodes on each edge is adjusted automatically, so that the total number of boundary nodes in each sub-domain is even, satisfying the necessary condition for generating all-quadrilateral mesh. For free constraint lines in each sub-domain, the method of regarding constraint lines as holes with zero area is proposed, so that constraint lines can be treated as internal boundaries. The merging method of constraint lines and outer boundary is given, which can deal with all possible distribution of constraint lines and has generality. The examples of mesh generation with a large number of constraint lines are given to demonstrate the reliability of proposed method.

CFD analysis of PWR core top and reactor vessel upper plenum internal subdomain models

One aspect of the Westinghouse AP1000™ 1 1 AP1000 is a trade mark of Westinghouse Electric Company, LLC. reactor design is the reduction in the number of major components and simplification in manufacturing. One design change relative to current Westinghouse reactors of similar size is that AP1000 reactor vessel has two nozzles/hot legs instead of three. With regard to fuel performance, this design difference creates a different flow field in the reactor vessel upper plenum. The flow exiting from the core and entering the upper plenum must turn toward one of the two outlet nozzles and flow laterally around numerous control rod guide tubes and support columns. Also, below the upper plenum are the upper core plate and the top core region of the 157 fuel assemblies and 69 guidetube assemblies. To determine how the lateral flow in the top of the core and upper plenum compares to the current reactors a CFD model of the flow in the upper portion of the AP1000 reactor vessel was created. Before detailed CFD simulations of the flow in the entire upper plenum and top core regions were performed, conducting local simulations for smaller sections of the domain provided crucial and detailed physical aspects of the flow. These sub-domain models were used to perform mesh sensitivities and to assess what geometrical details may be eliminated from the larger model in order to reduce mesh size and computational requirements. In this paper, CFD analysis is presented for two subdomain models: the top core region and control rod guide tube region. These models are chosen for simulation because guide tube and top core region (including top grid, top nozzle, and hold-down device) are the major components of upper plenum effecting the flow patterns and pressure distribution. The top core region, corresponding to ¼ of fuel assembly, includes components as upper part of the fuel assemblies (top grid, fuel rods, top nozzle), core component hold-down devices, and upper core plates. These components distribute the core flow to different sections of guidetube regions. Mesh sensitivity studies have been conducted for each individual part in order to determine the proper geometrical simplifications. Pressure drop measurement data are compared with the predicted CFD results and act as a guideline for the mesh selection. The guidetube region includes control rod guidetubes themselves, adjacent support columns and open regions. In this study, two models of subdomains are analyzed: (1) a ¼ section of one control rod guide tube by itself and (2) a representative unit cell containing two ¼ sections of adjacent control rod guide tubes and one ¼ section of a neighboring support column. Predicted flow rates at each of the outflow locations in conjunction with results from the mesh sensitivity studies provide guidance on (1) what geometry to preserve or remove, (2) what geometry can be simplified to reduce the required mesh, and (3) an estimate of the total mesh required to model the entire upper plenum and top fuel domain. The commercial CFD code STAR-CCM+ is employed to generate the computational mesh, to solve the Reynolds-averaged Navier–Stokes equations for incompressible flow with a Realizable k– ɛ turbulence model, and to post-process the results.

An improved cohesive element for shell delamination analyses

AbstractIn this paper, an improved cohesive element is proposed for accurate quantification of delamination in laminar composites. The improved cohesive element employs a mixed Gaussian and sub‐domain integration scheme for cohesive stress integration. Level set description of crack front geometry is used to accurately track the evolving delamination crack front. The new element offers significant improvement in solution accuracy and numerical stability, as compared with conventional cohesive elements using either Gaussian integration or Newton–Cotes integration. The much enhanced numerical accuracy and stability permit the use of bonded structural element size as large as 1∼1.5 times the cohesive zone size without significantly compromising numerical accuracy and efficiency. This greatly alleviates the strict mesh size requirement imposed by conventional cohesive elements that require the bonded structural element size be smaller than \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$\frac{1}{3}\sim\frac{1}{5}$\end{document} of the cohesive zone size. Furthermore, the new element offers the benefit of easy insertion of arbitrary initial crack geometry for a structured mesh. Copyright © 2010 John Wiley & Sons, Ltd.

A framework for cohesive element enrichment

It was shown in a previous work by the same authors that the stringent mesh size requirement on cohesive, interface elements, can be alleviated through enrichment of the finite element basis functions. In this paper, some limitations of the enriched formulation are discussed and a new maximum mesh size requirement is established. The enriched formulation is also applied here to the simulation of mixed-mode delamination for the first time.

Decohesion finite element with enriched basis functions for delamination

In order to address the stringent mesh size requirement of the cohesive element, currently 0.5mm or less, the mixed-mode interface finite element is enriched with the analytical solution of an idealized beam on elastic foundation. Both the interface and the solid continuum elements are enriched; the partition of unity (PU) method is utilized to obtain the enhanced interpolation, implemented with two user elements (UEL) in the commercial package ABAQUS/Standard. The new formulation yields predictions in excellent agreement with theoretical and experimental results for a typical mode I delamination benchmark, with elements 5mm in size.

Analysis of structural intensity of complex structures

The prediction and computation of the vibration structural intensity have been accomplished for simple structures, such as beams, rods, plates, and shells. These structures, even when connected to other simple structures, were amenable to analytic solutions, which allowed the researchers to obtain exact analytic expressions for the power flow and the structural intensity vector maps for these structures. A calculation of the structural intensity by the use of finite-element methods (FEM) is proposed. This hybrid method requires that one must delve into the FEM codes to retrieve all the resultant moments, shears, normal forces, as well as the transverse, tangential, and rotational velocities. These quantities are processed to result in complete structural intensity maps. The influence of mesh size, the use of resultants at the mid of the elements, and mesh size requirements as a function of axial, flexural, and torsional wavelengths are explored. An example of a connected branched structure undergoing coupled flexural, longitudinal, and torsional vibration is analyzed to illustrate the influence of these parameters on the accuracy of the structural intensity calculations.

An Analysis of Mesh Sizes Required for Screening Fishes at Water Intakes

Twenty-four species of marine and freshwater fish were examined to determine mesh size requirements for fish screens placed at water intakes. Curves relating fish length to the mesh size requirements are given for these species and a model for predicting mesh size requirements as a function of fish shape and size is presented. This is of superior accuracy in general application to a previous model given by Bell (1973) and appears to hold good for a wide range of fish species. Its practical application is discussed.