Search

This work is focused on the detection of interlayer damages in multi-layer composite materials, which use the inverse analysis approach based on the reduced-order models (ROMs). Direct problems including heat conduction through the solid and heat radiation to the space are solved by finite element method (FEM), and the solutions of transient nonlinear analysis are collected to build the snapshot data matrix. The Proper Orthogonal Decomposition (POD) method coupled with two surrogate models are utilized to construct a low dimensional model which can be used to rebuild physical fields. By minimizing the discrepancy of measured and simulated temperatures using ROMs, the optimal parameter values related to damages can be estimated efficiently. Results prove that an excellent estimation on the position of damages can be obtained in the multi-layer materials. The computational efficiency and solution accuracy of two ROMs are compared, which proves that the POD-Kriging method has faster convergence speed than the POD-RBF method, with the same fitness value. Moreover, noise analysis validates that two ROMs have similar stability, whereas the POD-Kriging method is easier to achieve convergence in this type of problems. [ABSTRACT FROM AUTHOR]

In this article, a completely new numerical method called the Local Least-Squares Element Differential Method (LSEDM), is proposed for solving general engineering problems governed by second order partial differential equations. The method is a type of strong-form finite element method. In this method, a set of differential formulations of the isoparametric elements with respect to global coordinates are employed to collocate the governing differential equations and Neumann boundary conditions of the considered problem to generate the system of equations for internal nodes and boundary nodes of the collocation element. For each outer boundary or element interface, one equation is generated using the Neumann boundary condition and thus a number of equations can be generated for each node associated with a number of element interfaces. The least-squares technique is used to cast these interface equations into one equation by optimizing the local physical variable at the least-squares formulation. Thus, the solution system has as many equations as the total number of nodes of the present heat conduction problem. The proposed LSEDM can ultimately guarantee the conservativeness of the heat flux across element surfaces and can effectively improve the solution stability of the element differential method in solving problems with hugely different material properties, which is a challenging issue in meshfree methods. Numerical examples on two- and three-dimensional heat conduction problems are given to demonstrate the stability and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. The computational results as presented in Part 1 have revealed some signatures of the basic algorithms, in which poor efficiency is its main shortcoming. In this article, as Part 2, several advanced algorithms are derived to high efficiently deal with the POD-based ROM of transient nonlinear heat conduction problems with temperature-dependent thermal conductivity, including: (i) Element pre-conversion method (EPM), (ii) Multi-level linearization method (MLM), and (iii) EPM–MLM compound method. The accuracy and efficiency are verified by both two-dimensional (2-D) and three-dimensional (3-D) numerical examples with Neumann boundary condition. The results show that these methods can provide high accuracy and high solution quality in the transient nonlinear heat conduction problems. Most importantly, the computational efficiency of these methods has been improved to different degrees when compared to that of the basic algorithm. Among them, the EPM–MLM compound method is the most efficient one. The acceleration effect of POD-based ROM solved by using this compound method is around one order of magnitude higher than that of the basic algorithm, and more pronounced for larger problems. [ABSTRACT FROM AUTHOR]

The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. Part 1 of this two-part articles presents the process and characteristics of basic algorithms, including POD explicit and implicit time-marching methods. The accuracy and efficiency are verified by several numerical examples with various boundary conditions and element types. The results show that the POD-based reduced order model (ROM) can provide high quality temperature prediction of the transient nonlinear heat conduction problems when using implicit method. However, the computational time of implicit method is much longer than that of explicit one. The acceleration effect of POD-based ROM on the calculation of the transient nonlinear heat conduction problems is one order of magnitude lower than that of the corresponding transient linear heat conduction problems. The improvement of computational efficiency is not pronounced. Further studies of the more efficient advanced algorithms to deal with POD-based ROM for transient nonlinear heat conduction problems will be presented in Part 2. Additionally, an approximate POD-based ROM for transient nonlinear heat conduction problem is proposed, which can be constructed quickly by using POD modes obtained from the corresponding transient linear heat conduction system. It is confirmed to be feasible for allowing nonlinear behavior to be modeled at an acceptable level of accuracy. It has significant application potential of solving practical engineering problems. [ABSTRACT FROM AUTHOR]

In this article, two types of new quadrilateral and hexahedron quadratic isoparametric elements are proposed for the element differential method (EDM) for solving heat conduction problems. These elements, called as the Ultra elements, have the minimum numbers of nodes comparing with the existing elements and have the feature that a central node is included inside them, which is necessary for the EDM analysis. The EDM is a strong-form method, which does not require control volumes and any integration. In the previous EDM for solving heat conduction problems, the Lagrange elements were used, which had many elemental nodes. The proposed new types of elements can circumvent this deficiency, in which only a few nodes are required. The shape functions for these elements are constructed for the first time, and the first and the second order derivatives of the shape functions with respect to intrinsic and global coordinates are analytically derived. Several 2D and 3D numerical examples are given to demonstrate the effectiveness, the accuracy and the efficiency of the newly proposed elements for the EDM for solving heat conduction problems. [ABSTRACT FROM AUTHOR]

A new radial integration boundary element method (RIBEM) for solving transient heat conduction problems with heat sources and variable thermal conductivity is presented in this article. The Green’s function for the Laplace equation is served as the fundamental solution to derive the boundary-domain integral equation. The transient terms are first discretized before applying the weighted residual technique that is different from the previous RIBEM for solving a transient heat conduction problem. Due to the strategy for dealing with the transient terms, temperature, rather than transient terms, is approximated by the radial basis function; this leads to similar mathematical formulations as those in RIBEM for steady heat conduction problems. Therefore, the present method is very easy to code and be implemented, and the strategy enables the assembling process of system equations to be very simple. Another advantage of the new RIBEM is that only 1D boundary line integrals are involved in both 2D and 3D problems. To the best of the authors’ knowledge, it is the first time to completely transform domain integrals to boundary line integrals for a 3D problem. Several 2D and 3D numerical examples are provided to show the effectiveness, accuracy, and potential of the present RIBEM. [ABSTRACT FROM PUBLISHER]

Purpose: Five patients presented to our institution with deep intraorbital foreign bodies adjacent to the optic nerve. We removed all foreign bodies by lateral orbitotomy to evaluate the treatment and the benefits of their extraction. Methods: The clinical outcomes of the five patients were retrospectively analyzed. Results: Radiology in all five patients revealed small foreign bodies touching the optic nerve in the deep orbital region. All patients also suffered from significant secondary psychological disturbances, these including anxiety and altered sleep patterns. They had become preoccupied with a strong desire to remove the intraorbital foreign bodies [IFB]. In this cohort, two had no light perception before surgery, another two had light perception, and one had hand motion perception as well as vitreous hemorrhage that had been plugged with silicone oil in other hospital. All foreign bodies were removed via lateral orbitotomy. Visual acuity improved after the operation in only three cases. However, the psychological well-being of all five patients improved. Conclusions: Consideration should be given to removal of intraorbital foreign bodies adjacent to the optic nerve, even where a significant degree of vision has already been lost. Furthermore some patients can achieved vision improvement and such surgery can frequently address the significant psychological disturbance that can be associated with such orbital foreign bodies. [ABSTRACT FROM AUTHOR]

A combined approach of the radial integration boundary-element method (RIBEM) and the precise algorithm in the time domain is presented for solving transient heat conduction problems with heat sources. First, by expanding physical quantities at discrete time intervals, the recursive formulations of the governing equation are derived. Then, the recursive equation is solved by the RIBEM. Finally, a self-adaptive check technique is carried out to estimate how many expansion terms are needed in a time-step size. Numerical results show that the present approach can obtain satisfactory performance. [ABSTRACT FROM PUBLISHER]