A new submodelling technique for multi-scale finite element computation of electromagnetic fields: application in bioelectromagnetism

Complex multi-scale Finite Element (FE) analyses always involve high number of elements and therefore require very long time of computations. This is caused by the fact, that considered effects on smaller scales have greater influences on the whole model and larger scales. Thus, mesh density should be as high as required by the smallest scale factor. New submodelling routine has been developed to sufficiently decrease the time of computation without loss of accuracy for the whole solution. The presented approach allows manipulation of different mesh sizes on different scales and, therefore total optimization of mesh density on each scale and transfer results automatically between the meshes corresponding to respective scales of the whole model. Unlike classical submodelling routine, the new technique operates with not only transfer of boundary conditions but also with volume results and transfer of forces (current density load in case of electromagnetism), which allows the solution of full Maxwell's equations in FE space. The approach was successfully implemented for electromagnetic solution in the forward problem of Magnetic Field Tomography (MFT) based on Magnetoencephalography (MEG), where the scale of one neuron was considered as the smallest and the scale of whole-brain model as the largest. The time of computation was reduced about 100 times, with the initial requirements of direct computations without submodelling routine of 10 million elements

Efficient multiscale methodology for local stress analysis of metallic railway bridges based on modal superposition principles

This paper presents an advanced submodelling methodology for local stress analysis of complex details of existing metallic railway bridges. The fatigue assessment of connections of large structures based on local methods leads inherently to a multiscale problem that can only be solved by adopting efficient numerical procedures. Aiming to overcome such limitations that influence the analysis process, submodelling techniques and modal superposition principles are combined to fully represent numerically the local geometrical, material and contact properties of the fatigue-critical details. The results of experimental in situ tests are proposed to characterise the numerical models and respective multiscale relation, implementing optimisation and validation procedures. In this work, the suggested efficient multiscale methodology for stress analysis aims to allow the subsequent local fatigue assessment, according to the real mechanism of loading transference, reducing sources of conservatism. All numerical procedures and respective validation thru experimental techniques are illustrated using a real case study.This work was financially supported by: Base Funding - UIDB/04708/2020 of the CONSTRUCT - Institute of R&D In Structures and Construction - funded by national funds through the FCT/MCTES (PIDDAC) and by national funds through FCT - Fundação para a Ciência e a Tecnologia; PD/BD/114101/2015. This work was also carried out in the framework of Shift2Rail projects IN2TRACK2 [826255-H2020-S2RJU-CFM-2018] and IN2TRACK3 [101012456-H2020-S2RJU-CFM-2020].info:eu-repo/semantics/publishedVersio

Cyclic J-integral using the linear matching method

The extended version of the latest Linear Matching Method (LMM) has the capability to evaluate the stable cyclic response, which produces cyclic stresses, residual stresses and plastic strain ranges for the low cycle fatigue assessment with cyclic load history. The objective of this study is to calculate ΔJ through the LMM and suggest future development directions. The derivation of the ΔJ based on the potential energy expression for a single edge cracked plate subjected to cyclic uniaxial loading condition using LMM is presented. To extend the analysis so that it can be incorporated to other plasticity models, material Ramberg-Osgood hardening constants are also adopted. The results of the proposed model have been compared to the ones obtained from Reference Stress Method (RSM) for a single edge cracked plate and they indicate that the estimates provide a relatively easy method for estimating ΔJ for describing the crack growth rate behaviour by considering the complete accumulated cycle effects

Development of Methodologies for the Solution of the Forward Problem in Magnetic-Field Tomography (MFT) Based on Magnetoencephalography (MEG)

The prime topic of research presented in this report is the development and validation of methodologies for the solution of the forward problem in Magnetic field Tomography based on Magnetoencephalography. Throughout the report full aspects of the accurate solution are discussed, including the development of algorithms and methods for realistic brain model, development of realistic neuronal source, computational approaches, and validation techniques. Every delivered methodology is tested and analyzed in terms of mathematical and computational errors. Optimizations required for error minimization are performed and discussed. Presented techniques are successfully integrated together for different test problems. Results were compared to experimental data where possible for the most of calculated cases. Designed human brain model reconstruction algorithms and techniques, which are based on MRI (Magnetic Resonance Imaging) modality, are proved to be the most accurate among existing in terms of geometrical and material properties. Error estimations and algorithm structure delivers the resolution of the model to be the same as practical imaging resolution of the MRI equipment (for presented case was less than 1mm). Novel neuronal source modelling approach was also presented with partial experimental validation showing improved results in comparison to all existing methods. At the same time developed mathematical basis for practical realization of discussed approach allows computer simulations of any known neuronal formation. Also it is the most suitable method for Finite Element Method (FEM) which was proved to be the best computer solver for complex bio-electrical problems. The mathematical structure for Inverse problem solution which is based on integrated human brain modelling technique and neuronal source modelling approach is delivered and briefly discussed. In the concluding part of the report the practical application case of developed techniques is performed and discussed

Optimisation of postbuckling stiffened composite structures

The thesis starts off with an introductory chapter on composite materials. This includes a definition of composites, a brief history of composite materials, their use in aerostructures (primarily as stiffened structures), and also optimization of composite structures. A literature review is then presented on postbuckling stiffened structures. This includes both experimental investigations on stiffened composite panels and investigations into secondary instabilities and mode jumping as well as their numerical modelling. Next, the Finite Element (FE) modelling of posthuckling stiffened structures is discussed, relating how ABAQUS models are set up in order to trace stiffened composite panels' buckling and postbuckling responses. An experimental programme conducted on an I-stiffened panel is described, where the panel was tested in compression until collapse. The buckling and postbuckling characteristics of the panel are presented, and then an FE model is described together with its predicted numerical behaviour of the panel's buckling and postbuckling characteristics. Focus then shifts to the modelling of failure in composites, in particular delamination failure. A literature review is conducted, looking at the use of both the Virtual Crack Closure Technique (VCCT) and interface elements in delamination modelling. Two stiffener runout models, representing two specimens previously tested experimentally, are then developed to illustrate how interface elements may be used to model mixed mode delamination. The previously discussed panel is revisited, and a global-local modelling approach used to model the skin-stiffener interface. FE models of a stiffened cylindrical shell are also considered, and again the postbuckling characteristics of the shell are compared with experimental results. . The thesis then moves on to optimization of composite structures. This starts off with a literature review of existing optimization methodologies. A Genetic Algorithm (GA) is devised to increase the damage resistance of the I-stiffened panel. The global-local ABAQUS model discussed earlier is used in conjunction with the GA in order to find a revised stacking sequence of both the panel flanges and skin so as to minimize skin-stiffener debonding subject to a variety of design constraints. A second optimization is then presented, this time linked to the FE model of the stiffened cylindrical shell. The objective is to increase the collapse load of the shell, again subject to specific design constraints. The thesis concludes by summarising the importance of the work conducted. FE models were created and validated against experimental work in order to model a variety of composite stiffened structures in their buckling and postbuckling regimes. These models were able to capture the failure characteristics of these structures relating to delamination at the skin-stiffener interface, a phenomenon widely observed experimentally. Various optimizations, able to account for failure mechanisms which may occur prior to overall structural collapse, were then conducted on the analysed structures in order to obtain more damage resistant designs.Imperial Users onl

Stress Analysis of an Endosseus Dental Implant by BEM and FEM

In this work the Boundary Element Method (BEM) and the Finite Element Method (FEM) have been used for an elastic-static analysis of both a Branemark dental implant and a generic conic threaded implant, modelled either in the complete mandible or in a mandibular segment, under axial and lateral loading conditions. Two different hypotheses are considered with reference to degree of osteo-integration between the implant and the mandibular bone: perfect and partial osteointegration. The BEM analysis takes advantage of the submodelling technique, applied on the region surrounding the implant. Such region is extracted from the overall mandible and the boundary conditions for such submodel are obtained from the stress analysis realised on the complete mandible. The obtained results provide the localisation of the most stressed areas at the bone-implant interface and at the mandibular canal (containing the alveolar nerve) which represent the most critical areas during mastication. This methodology, enriched with the tools necessary for the numerical mandible reconstruction, is useful to realise sensitivity analysis of the stress field against a variation of the localisation, inclination and typology of the considered implant, in order to assess the optimal implant conditions for each patient under treatment. Due to the high flexibility in the pre- and post-processing phase and accuracy in reproducing superficial stress gradients, BEM is more efficient than FEM in facing this kind of problem, especially when a linear elastic constitutive material law is adopted

Micro-indentation based study on steel sheet degradation through forming and flattening: Toward a predictive model to assess cold recyclability

In Cold Roll Forming (CRF) process sheet material undergo a complex set of deformation that entail complicated through thickness residual deformation. This paper, focuses on material behaviour in CRF processes, with regarding damage and material degradation. A roll forming process is taken as case study and experimental investigation using extensive microhardness mapping alongside FE simulation of the process are the basis of material damage study. Indentation on different cross-sectional cutting angles -45, 0, 45 has been performed to study the sensitivity to orientation and crystallographic texture. A 3D Finite Element simulation with emphasis on through-thickness variation of the plastic deformation was carried out, using multiple layers of solid elements representing the sheet. A smart approach to reduce computational cost was employed in MSC.Marc by implementing simulation of a master model of complete material with shell elements, followed by partial sub-modelling comprising solid elements in regions of interest. This cross-sectional hardness map was then converted to the corresponding equivalent plastic strain in the cross section for validation. The correlation factor between Hardness and yield stress was discussed

fatigue crack growth in a compressor stage of a turbofan engine by fem dbem approach

Abstract In this work, the fatigue crack-growth process in a rotating disk of an aircraft gas turbine engine has been simulated. The considered crack nucleated in the attachment between a blade and the disk of a compressor stage, both made of a two-phase titanium alloy. The fatigue crack-growth process of such crack has been simulated by means of two codes, ABAQUS and BEASY, based on Finite Element Method (FEM) and Dual Boundary Element Method (DBEM) respectively. In particular, a variant of the submodelling technique, based on the superposition principle, has been used for coupling the two codes in order to exploit simultaneously their peculiar strength points. The FEM code has been used to compute the global stress field whereas the DBEM code has been used to calculate the fracture parameters, useful to predict the crack-growth evolution. The J-integral method and the Minimum Strain Energy Density Criterion (MSED) have been used for calculating K values and predicting crack kinking respectively. In this work, the FEM-DBEM crack path is compared with both the path obtained by a full-scale experimental test and the path predicted via a full FEM approach: having in an initial stage considered the only centrifugal load, with no allowance e.g. for the fluid pressure on the blades and for the blade dynamic behaviour, some discrepancies are found between numerical and experimental results. The computational advantages of the proposed submodelling approach are highlighted, in addition to a preliminary fatigue assessment provided for the considered compressor disk (further analyses are under development)