Domain decomposition based finite element verification in linear framework

PurposeThis paper aims to deal with the verification of local quantities of interest obtained through linear elastic finite element analysis. A technique is presented for determining the most accurate error estimation. This technique enables one to address industrial‐size problems while keeping computing costs reasonable.Design/methodology/approachThe concept of error in constitutive relation is used to assess the quality of the finite element solution. The key issue is the construction of admissible fields. The objective is to show that it is possible to build admissible fields using a new method. These fields are obtained by using a high‐quality construction over a limited zone while the construction is less refined and less expensive elsewhere.FindingsNumerical tests are presented in order to illustrate a very satisfying presented methodology. It shows clearly how to take advantage of the method to treat large examples. They clearly show the interest of this new method to treat large examples.Originality/valueThe paper demonstrates clearly that verification of large finite element problem must have dedicated methods in order to be applicable.

Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems

Fast estimation of discretization error for FE problems solved by domain decomposition

The settlement prediction of small pile group at working load using 3D Finite Element (FE) approach was carried out based on the case of Belfast pile load test. Three different types of analysis were investigated: a linear elastic (LE) analysis where all the soil was assumed to be linear elastic, a complete nonlinear (CNL) analysis where both the soil adjacent to the pile shafts and between the piles using the Hardening Soil (HS) model, and a nonlinear and linear elastic analysis (NL-LE) with the soil close to the pile shafts using HS model while the soil in the remaining area is modeled as an elastic material. Then all the FE analyses were compared to the analytical approach (RATZ). The results of FE analysis suggest that incorporating a nonlinear zone of soil close the pile shaft and leaving the soil linear elastic beyond this zone gives more reasonable estimation of interaction factor, thus, a much better prediction of pile group settlement will be observed. It is suggested that a value of half the pile width for the distance from pile shaft to the edge of this nonlinear zone would be sufficient to capture the load transfer mechanism for a typical pile group. While best prediction was given by RATZ approach as the group settlement ratio which reflect the interaction effect between piles in the group obtained from RATZ mostly close to the field measurements.

Updating 2D acoustic models with the constitutive relation error method

The strength of T-tubular joints with elliptical and circular cross-section tube chords with circular cross-section tube braces has been investigated. Experimental tests to determine the joint strength of these T-joints subjected to tension, compression, in-plane bending and out-of-plane bending loading cases have been carried out. A rig has been designed and built for that purpose. Three types of T-joint connections, namely type 1, type 2 and type 3, were selected. In type 1, the joint consisted of braces welded perpendicularly to the circular chord outer diameter, while for type 2 the brace had been welded perpendicularly to the elliptical chord minor diameter and for type 3 the brace has been welded perpendicularly to the elliptical chord major diameter. The chord has been held as fixed-fixed for all types. The material used in all tubes tested was mild steel. Throughout this investigation the ultimate loads and ultimate moments obtained from the tests have been converted to non-dimensional strength values for fair comparisons. Finite element models for similar T-joints for the three types were created and used under the same loading cases. Shell elements have been used to model the mesh required. An elastic analysis has also been carried out. The experimental results obtained show that type 3 joints are stronger than type 1 for all the loading modes. The increase in load and moment varies from 12.16 to 27.27 per cent. On the other hand, type 2 joints were found to be weaker than type 1 joints by 7.5-27.68 per cent for different loading modes. A comparison between experimental results and finite element analysis has also been made. It shows a percentage variation of 0.89-34.40 per cent. Another comparison with existing tubular joint design formulae showed that these formulae are conservative and highly safe for the geometry used.

The present work is concerned with three-dimensional finite element analysis of the hollow section extrusion process using a porthole die. The effects of related design parameters are discussed through the finite element simulation for extrusion of a triply-connected rectangular tubular section. For economic computation, mismatching refinement, an efficient domain decomposition method with different mesh density for each subdomain, is implemented. In order to obtain the uniform flow at the outlet, design parameters such as the hole size and the hole position are investigated and compared through the numerical analysis. Comparing the velocity distribution with that of the original design, it is concluded that the design modification enables more uniform flow characteristics. The analysis results are then successfully reflected on the industrial porthole die design

We present a thermomechanical model of a laminated string for the optimization of interconnects for modules with back contact silicon solar cells. First we calculate the thermal stresses in a laminate of 9 noninterconnected cells that result from the cooling process from lamination temperature of 150°C down to −40°C. In a second step we add the interconnectors in a 2-dimensional geometry which is bidirectionally coupled to the original 3-dimensional geometry of the laminated cell string. Both simulations show the resulting stresses on the solar cells and all other module components. The first analysis shows the same stress distribution for every cell in the string. In the second simulation we find the cell stresses near the 3 soldered areas to depend significantly on the specific interconnector design. The model presented here consists of the equations from continuum mechanics and is solved by Finite Element Analysis. In this modeling approach we describe the mechanical material behavior by linear elasticity. The 2-dimensional plain-stress modeling of the interconnector allows fast and easy modifications of the interconnector’s design and helps to estimate the mechanical performance of the interconnector as a part of the 3dimensional string. In a last step the electrical performance of the interconnector is simulated.

We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error (CRE) to obtain a guaranteed and fully computable a posteriori error estimate in the energy norm (as well as error indicators on various error sources). Here, the CRE concept is coupled with the solution of an adjoint problem to control the error and drive an adaptive procedure with respect to a given output of interest. Furthermore, a local and non-intrusive enrichment technique is proposed to enhance the accuracy of error bounds. The overall strategy, which is fully automatic and robust, enables to reach an appropriate trade-off between certified reliability and computational cost in the MsFEM context. The performances of the proposed method are investigated on several illustrative numerical test cases. In particular, the error estimation is observed to be very accurate, yielding a very efficient adaptive procedure.

Objective To explore the establishment of 3D thoracic model by finite element methods, and study the mechanical mechanism of minimally invasive surgery for correcting the chest wall deformity, and provide personalized surgery solution in the future. Methods According to admission and exclusion criteria, we selected 10 cases of pectus carinatum that received chest CT scan. The finite element model of pectus carinatum was established and analyzed by Mimics, ABAQUS, etc. The validity of finite element method for chest wall was verified by comparing the sternal displacement between the simulated values and actual values with the same force. Results The 3D finite element model of pectus carinatum was successfully established and analyzed. The stress distribution of the 10 cases in the posterior ribs was mainly in the 1-6 ribs on both sides, mostly concentrated in the 4th to 6th ribs, and the stress was symmetrical on both sides. Statistical analysis showed that the displacement value of the sternum was correlated, and the validity of the model was verified. Conclusion Mimics, ABAQUS and other finite element modeling and analysis software can effectively establish the thoracic 3D finite element model and mechanical analysis, which can help the further development of personalized minimally invasive surgery for correcting chest wall deformities. Key words: Pectus carinatum; Chest wall deformity; Finite element analysis

Fracture mechanics analysis using the finite element method has been one of the key methodologies to evaluate structural integrity for aging infrastructures such as aircraft, ship, power plants, etc. However, three-dimensional crack analyses for structures with highly complex three-dimensional shapes have not widely been used, because of many technical difficulties such as the lack of enough computational power. The authors have been developing a fracture mechanics analysis system that can deal with arbitrary shaped cracks in three-dimensional structures. The system consists of mesh generation software, a finite element analysis program and a fracture mechanics module. In our system, a Virtual Crack Closure-Integral Method (VCCM) for the quadratic tetrahedral finite elements is adopted to evaluate the stress intensity factors. This system can perform the three-dimensional fracture analyses. Fatigue and SCC crack propagation analyses with more than one cracks of arbitrary complicated shapes and orientations. The rate and direction of crack propagation are predicted by using appropriate formulae based on the stress intensity factors. When the fracture mechanics analysis system is applied to the complex shaped aging structures with the cracks which are modeled explicitly, the size of finite element analysis tends to be very large. Therefore, a large scale parallel structural analysis code is required. We also have been developing an open-source CAE system, ADVENTURE. It is based on the hierarchical domain decomposition method (HDDM) with the balancing domain decomposition (BDD) pre-conditioner. A general-purpose parallel structural analysis solver, ADVENTURE_Solid is one of the solver modules of the ADVENTURE system. In this paper, we combined VCCM for the tetrahedral finite element with ADVENTURE system and large-scale fracture analyses are fully automated. They are performed using the massively parallel super computer ES2 (Earth Simulator 2) which is owned and run by JAMSTEC (Japan Agency for Marine-Earth Science and Technology).

SummaryThis article deals with the computation of guaranteed lower bounds of the error in the framework of finite element and domain decomposition methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a domain decomposition iterative solver) from the discretization error (due to the finite element), which enables the steering of the iterative solver by the discretization error. These lower bounds are also used to improve the goal‐oriented error estimation in a substructured context. Assessments on 2D static linear mechanic problems illustrate the relevance of the separation of sources of error and the lower bounds' independence from the substructuring. We also steer the iterative solver by an objective of precision on a quantity of interest. This strategy consists in a sequence of solvings and takes advantage of adaptive remeshing and recycling of search directions. Copyright © 2016 John Wiley & Sons, Ltd.

The aim of this study is to analyze the possibilities to measure the wall stress on the thinnest and thickest side of the AAA by using patient’s Specific Finite Element (SFE) models, in order for understanding the rupture of AAA in a better approach. Patient specific model with different in position, Finite Element Analysis (FEA) models that were studied earlier by Di Martino et al. (1998) [ 1 ], was adopted. The AAA was modelled as a homogenous, isotropic, incompressible, linear elastic material with Young’s modulus (E) and Poisson’s ratio (µ) having value of 0.11 MPa and µ = 0.45, respectively. The values of E and µ was determined from uniaxial loading tests performed on specimens of AAA. In order to cast peak systolic blood pressure of a healthy patient, pressure of 145 mmHg was directed to the internal surface of the models. FEA models of AAA were analysed using ANSYS Finite Element Package 15.0 version. Values of stress was observed on the scale of von-Mises, this method helps to locate area with highest stress i.e. to calculate failure criteria by combining the stress in three-dimensions. In order to determine the collapse of AAA wall von-Mises stress is commonly use for the assessment of the AAA stress. Our findings and results strengthens the earlier studies performed by Polzer et al. (2010) [ 2 ] and Altuwaijri (2015) [ 3 ], where AAA wall stress was reduced by formation of thrombus. Thus reducing the chance of AAA rupture and supporting the wall strength. Our findings suggest that thrombus clearly works as a shield to guard the AAA wall from rupture. However, more research and further studies are required that corroborate the relation between the biological and mechanical factors to understand the role of the thrombus for AAA rupture.

Distributed finite element calculations on transputer arrays and the DAP

Advances in Adaptive Computational Methods in Mechanics