AI-Enhanced Finite Element Method (FEM) for Structural Analysis

An accurate evaluation of the dynamic responses on critical components of orthotropic bridge decks is of significance for identifying structural damage and predicting the fatigue life of long-span cable-stayed bridges. However, the traditional finite element (FE) methods are computationally cost-prohibitive for this application. In response, a new multiscale time-varying analysis method based on the dynamic balance equations and FE strategies is proposed and derived theoretically in this paper. Unlike most existing methods, the dynamic responses of this refined model is easily solved through repeated iterations, using the dynamic responses of a large-scale model as the boundary conditions. To validate the effectiveness of the method, a simply supported steel plate beam was used in a field test that demonstrated good correlation between the analytical dynamic responses and the experimental ones. To further validate this method, a case study involving a whole segment model of the Pingtan Bridge orthotropic bridge deck was established and the complex junction area between the plate and longitudinal ribs was modeled using two refinement processes. For comparison, a sufficiently refined model was also developed using ANSYS software based on the traditional FE methods. This study attempted to provide a new high-efficiency analysis framework for accurate analysis of local vibration problems. Under relatively small and easily manageable calculation conditions at each cross-scale processing level, the proposed method meets not only the requirements of global design for actual engineering applications, but also supports further in depth analysis.

Temperature change of liquid stratification for LNG tank is more complex; therefore, it is necessary to carry out temperature field analysis of liquid stratification for LNG tank, and the orthogonal ridgelet finite element method is constructed by combining the traditional finite element method and orthogonal ridgelet transformation. Firstly, the basic characteristics of orthogonal ridgelet transform are studied. Secondly, the theory models of liquid stratification of LNG tank are studied. Thirdly, the temperature field analysis model of liquid stratification orthogonal ridgelet finite element for LNG tank is constructed. Finally, the temperature field analysis of liquid stratification of LNG tank is carried out, and the temperature changing rules of liquid stratification for LNG tank are obtained based on the traditional finite element method, B-spline wavelet finite element method, orthogonal ridgelet finite element method, and field test, and comparison of results shows that the orthogonal ridgelet finite element method has highest computing precision and efficiency. In addition, the effect of leakage heat intensity on time of rolling caused by liquid stratification of LNG tank is obtained.

In traditional finite element methods, a common hypothesis is the nodes of an element being fixed with material points, which place restrictions on the description of a system. In this paper, this hypothesis is released and a new kind of rope element with nodes being no longer fixed with either spatial coordinates or material coordinates is presented. The theory of obtaining material velocity and acceleration of a point from the corresponding spatial velocity and acceleration of the point is established. The velocities and accelerations in the principle of virtual power should being material velocities and accelerations respectively is emphasized and applied. According to the feature of a rope-pulley system, its movement can be described by a new group of variables, such as arc-lengths, azimuthal angles and strains of ropes at entrance and exit contacting points. Instead of traditional methods, conditions of contact between rope and pulley are modeled as the material velocity of a point on the contacting rope being equal to the corresponding point on the pulley. By means of the presented methods, some obstacles, such as frequently divergence and high time consuming that resulting from traditional finite element methods can be removed. Motion equation of the rope-pulley system is derived by the principle of virtual power. Arc-length coordinates, positions of contact boundary points, the movement of pulley centers and their body-fixed reference coordinate systems, shape and positions changing of ropes as well as the tension forces in every point of a rope, can be obtained high precisely. The presented method can provide a new theoretical basis for analysis of mechanical systems with ropes and pulleys. The presented theory of using spatial points as describing variables to replace traditional material points is of applicable widely. It can be a reference for theory and application of finite element methods.

Based on the model of rigid-spring element suitable for homogeneous elastic problem, which was developed by Japanese professor Kawai, the interface stress element model (ISEM) for solving the problem of discontinuous media mechanics has been established. Compared with the traditional finite element method (FEM), the ISEM is more accurate and applicable. But the total number of freedom degree of ISEM in dealing with three-dimensional problems is higher than that of FEM, which often brings about the reduction on efficiency of calculation. Therefore, it is necessary to establish a mixed model by gathering the advantages of ISEM and FEM together. By making use of the good compatibility of ISEM and introducing the concept of transitional interface element, this paper combines ISEM and FEM and proposes a mixed model of ISEM-FEM which can solve, to a large extent, the contradictions between accuracy and efficiency of calculation. In addition, using natural coordinate, algorithm of ISEM for block elements of arbitrary shape has been performed. Numerical examples show that the method proposed in this paper is feasible and its accuracy is satisfactory.

The boundary element method for elasticity problems with concentrated loads based on displacement singular elements

SummaryThis paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.

The cooling rule of the crude oil in the storage tank is studied by using the new wavelet finite element method, the traditional finite element method, and a test. First, a computational model is presented. Then the cooling rule of the crude oil is provided experimentally and numerically under the liquid levels of 6.5 and 11.5 m, respectively, and the results show that the wavelet finite element method has higher reliability. Then, the longitudinal distribution rule of the temperature of the crude oil in the storage tank under different liquid levels is obtained. Last, the cooling mechanism of the crude oil is provided.

A novel adjustable degrees-of-freedom numerical method for computing the temperature distribution of electrical devices is presented. The proposed method provides a convenient, accurate and efficient approach to increase/reduce variables and couple/decouple variables. In traditional finite element method (FEM), the electromagnetic field and thermal field need different FEM meshes, which reduce the efficiency and accuracy of the field coupling. Also, the traditional method introduces the inevitable error when the power loss is plotted from Maxwell to Fluent as the different meshes are employed. In this paper, the greatest advantage is that the electromagnetic field and thermal field can be computed using a single mesh with the proposed technology of exploiting different constrained degrees-of-freedom, which decreases the computation time and system complexity. The global domain divided into several sub-domains were utilizing various corresponding functions and also employed to reduce the computational burden when calculating the core loss, copper loss, stray loss and temperature distribution. Numerical examples are reported to showcase the accuracy and effectiveness of the proposed method.

Applications of magnetic-resonant wireless power transfer technology have been extensively researched because of its high efficiency, security and convenience. To recharge batteries, the induced ac voltage in the receiver coil of wireless systems must be rectified to dc, hence the power transfer systems are inevitably nonlinear. In this paper, a novel approach based on time-domain finite element method (FEM) is presented to analyze the nonlinear system in order to obtain frequency-sweeping solutions quickly. At the first step of the proposed method, the wireless power transfer system, excluding the rectifier circuit, will be equivalent to a voltage source and a general impedance at different frequencies. The equivalent circuit is then connected to the rectifier circuit. Numerical example being reported in this paper indicates that the results obtained using the proposed methodology are consistent with those obtained using traditional time-domain FEM method. If solutions at different operating frequencies are required, the proposed method can save a lot of computation time, because one just needs to solve the field problem using the time-domain FEM twice. From the numerical example on the performance analysis of the wireless power transfer system being studied, the computing time of the proposed time-domain method is only 2% of that required if traditional time-domain FEM method is used.

Machine learning based digital twin for dynamical systems with multiple time-scales

A node-moving algorithm with application to Burgers equation and the Moltz problem

The Hartree–Fock equations for atoms are solved with the p version of the finite element method, which differs from the traditional finite element method in using high order, hierarchic polynomials as basis functions. Recursion formulas are developed for the analytical evaluation of integrals, which are crucial in reducing the computation time and maintaining the accuracy of the solution. A hierarchic computational approach is used where the solution at a certain level is used to start the calculation at the next level. Results are presented for closed and open shell atoms taken from various columns of the periodic table that show excellent agreement with accurate numerical calculations.

Vectorial finite element method for neutron transport solving with preconditioning GMRES acceleration

Accurate simulation of electrostatic field in electronic devices is very important to improve their performance. When the traditional finite element method is used to analyze the electrostatic field of large and complex structures, the calculation speed is slow and the computing resources are greatly consumed. Therefore, in this paper, we investigate electrostatic analysis with a non-overlapping domain decomposition method based on the scalar finite element method under a novel transmission condition. In order to improve the efficiency of matrix solving and reduce the memory consumption, the block Jacobi preconditioner is introduced. In addition, the multifrontal block incomplete Cholesky preconditioner is utilized to further improve the computational performance based on the block Jacobi preconditioner. Several numerical examples are simulated and compared with the analytical solutions and the commercial software Maxwell 3D. The results demonstrate the accuracy and efficiency of the proposed domain decomposition method.

This paper provides a simple numerical method to determine the optimal parameters of tuned mass damper (TMD) and viscoelastic dampers (VEDs) in frame structure for wind vibration control considering the soil-structure interation (SSI) effect in frequency domain. Firstly, the numerical model of frame structure equipped with TMD and VEDs considering SSI effect is established in frequency domain. Then, the genetic algorithm (GA) is applied to obtain the optimal parameters of VEDs and TMD. The optimization process is demonstrated by a 20-storey frame structure supported by pile group for different soil conditions. Two wind resistant systems are considered in the analysis, the Structure-TMD system and the Structure-TMD-VEDs system. The example proves that this method can quickly determine the optimal parameters of energy dissipation devices compared with the traditional finite element method, thus is practically valuable.