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Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

The goal of this work is to create a computational finite element model to perform thermoelastic stress analysis (TSA) with the usage of a non-ideal load frequency, containing the effects of the material thermal properties.

Throughout this document, the methodology of the model is presented first, followed by the procedure and results. The last part is reserved to results, discussion and conclusions.

This work had the main goal to create a model to perform TSA with the usage of non-ideal loading frequencies, considering the materials’ thermal properties. Loading frequencies out of the ideal range were applied and the model showed capable of good results. The created model reproduced acceptably the TSA, with the desired conditions.

This work creates a model to perform TSA with the usage of non-ideal loading frequencies, considering the materials’ thermal properties.

This paper aims to solve inhomogeneous dielectric problems by matching boundary conditions at the interfaces among homogeneous subdomains. The capabilities of Hilbert transform computations are deeply investigated in the case of limited numbers of samples, and a refined model is presented by means of investigating accuracies in a case study with three subdomains.

The accuracies, refined by Richardson extrapolation to zero error, are compared to finite element (FEM) and finite difference methods. The boundary matching procedures can be easily applied to the results of a previous Schwarz–Christoffel (SC) conformal mapping stage in SC + BC procedures, to cope with field singularities or with open boundary problems.

The proposed field computations are of general interest both for electrostatic and magnetostatic field analysis and optimization. They can be useful as comparison tools for FEM results or when severe field singularities can impair the accuracies of other methods.

This static field methodology, of course, can be used to analyse transverse electro magnetic (TEM) or quasi-TEM propagation modes. It is possible that, in some case, these may make a contribution to the analysis of axis symmetrical problems.

The most relevant result is the possible introduction of SC + BC computations as a standard tool for solving inhomogeneous dielectric field problems.

The combined effects of several complex phenomena cause the deterioration of elements in steel hydraulic structures (SHSs) within the US lock system: corrosion, cracking and fatigue, impact and overloads. Predicting the future condition state of these structures by the use of current condition state inspection data can be achieved through the probabilistic chain deterioration model. The purpose of this study is to derive the transition probability matrix using final elements modeling of a miter gate.

If predicted accurately, this information would yield benefits in determining the need for rehabilitation or replacement of SHS. However, because of the complexity and difficulties on obtaining sufficient inspection data, there is a lack of available condition states needed to formulate proper transition probability matrices for each deterioration case.

This study focuses on using a three-dimensional explicit finite element analysis (FEM) of a miter gate that has been fully validated with experimental data to derive the transition probability matrix when the loss of flexural capacity in a corroded member is simulated.

New methodology using computational mechanics to derive the transition probability matrices of navigation steel structures has been presented.

The difficulty of deriving the transition probability matrix to perform a Markovian analysis increases when limited amount of inspection data is available. The used state of practice FEM to derive the transition probability matrix is not just necessary but also essential when the need for proper maintenance is required but limited amount of the condition of the structural system is unknown.

This paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.

Single-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.

The width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.

This study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

The purpose of the work is to provide a comprehensive review of the digital image correlation (DIC) technique for those who are interested in performing the DIC technique in the area of manufacturing.

No methodology was used because the paper is a review article.

no fundings.

Herein, the historical development, main strengths and measurement setup of DIC are introduced. Subsequently, the basic principles of the DIC technique are outlined in detail. The analysis of measurement accuracy associated with experimental factors and correlation algorithms is discussed and some useful recommendations for reducing measurement errors are also offered. Then, the utilization of DIC in different manufacturing fields (e.g. cutting, welding, forming and additive manufacturing) is summarized. Finally, the current challenges and prospects of DIC in intelligent manufacturing are discussed.

The purpose of this study concerns numerical studies and experimental validation of the mechanical behavior of hybrid specimens. These kinds of composite specimens are made up of thin carbon and glass substrates on which some Macro Fiber Composite^® (MFC) piezoelectric patches are glued. A proper design and manufacturing of the hybrid specimens as well as testing activities have been performed. The research activity has been carried out under the FutureWings project, funded by the European Commission within the 7th Framework.

The paper describes the basic assumptions made to define specimen geometries and to carry out experimental tests. Finite element (FE) results and experimental data (laser technique measurements) have been compared: it shows very good agreement for the displacements’ distribution along the specimens.

Within the objectives of the project, the study of passive and active deformation characteristics of the hybrid composite material has provided reference technical data and has allowed for the correct adaptation of the FE models. More in particular, using the hybrid specimens, both the bending deformations and the torsion deformations have been studied.

The deformation capability of the hybrid specimens will be used in the development of prototypical three-dimensional structures, that, through the electrical control of the MFC patches, will be able to change the curvature of their cross section or will be able to change the angle of torsion along their longitudinal axis.

The design of nonstandard specimens and the tests executed represent a novelty in the field of structures using piezoelectric actuators. The numerical and experimental data of the present research constitute a small step forward in the field of smart materials technology.