Structural finite-element analysis (FEA) has been widely used to study the biomechanics of human tissues and organs, as well as tissue–medical device interactions, and treatment strategies. However, ...patient-specific FEA models usually require complex procedures to set up and long computing times to obtain final simulation results, preventing prompt feedback to clinicians in time-sensitive clinical applications. In this study, by using machine learning techniques, we developed a deep learning (DL) model to directly estimate the stress distributions of the aorta. The DL model was designed and trained to take the input of FEA and directly output the aortic wall stress distributions, bypassing the FEA calculation process. The trained DL model is capable of predicting the stress distributions with average errors of 0.492% and 0.891% in the Von Mises stress distribution and peak Von Mises stress, respectively. This study marks, to our knowledge, the first study that demonstrates the feasibility and great potential of using the DL technique as a fast and accurate surrogate of FEA for stress analysis.
We present equilibrated flux a posteriori error estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two-dimensional ...Poisson problem. Relying on the equilibration by the mixed finite element solution of patchwise Neumann problems, the estimates are guaranteed, locally computable, locally efficient, and robust with respect to polynomial degree. Maximal local overestimation is guaranteed as well. Numerical experiments suggest asymptotic exactness for the incomplete interior penalty discontinuous Galerkin scheme.
During the Selective Laser Melting (SLM) process large temperature gradients can form, generating a mismatch in elastic deformation that can lead to high levels of residual stress within the ...additively manufactured metallic structure. Rapid melt pool solidification causes SLM processed Ti6Al4V to form a martensitic microstructure with a ductility generally lower than a hot working equivalent. Currently post-process heat treatments can be applied to SLM components to remove in-built residual stress and improve ductility.
This study examined the effect of scanning strategy (scan vector lengths and scan vector rotation) and rescanning strategy on residual stress formation and mechanical properties of SLM Ti6Al4V parts. 90° alternating scanning strategy resulted in the lowest residual stress build-up for SLM Ti6Al4V parts built on both the standard and modified Renishaw platforms using a modulated Nd-YAG fiber laser. Scanning strategy did not show any direct correlation with mechanical properties. Re-scanning with 150% energy density resulted in 33.6% reduction in residual stress but the effect on mechanical properties was detrimental and samples failed prematurely. The study was based on detailed experimental analysis along with Finite Element simulation of the process using ABAQUS to understand the underlying physics of the process.
This paper introduces a finite element method by using a weakly defined gradient operator over generalized functions. The use of weak gradients and their approximations results in a new concept ...called discrete weak gradients which is expected to play an important role in numerical methods for partial differential equations. This article intends to provide a general framework for managing differential operators on generalized functions. As a demonstrative example, the discrete weak gradient operator is employed as a building block in the design of numerical schemes for a second order elliptic problem, in which the classical gradient operator is replaced by the discrete weak gradient. The resulting numerical scheme is called a weak Galerkin (WG) finite element method. It can be seen that the weak Galerkin method allows the use of totally discontinuous functions in the finite element procedure. For the second order elliptic problem, an optimal order error estimate in both a discrete H1 and L2 norms are established for the corresponding weak Galerkin finite element solutions. A superconvergence is also observed for the weak Galerkin approximation.
Accurate muscle geometry is essential to estimate moment arms in musculoskeletal models. Given the complex interactions between shoulder structures, we hypothesized that finite element (FE) modelling ...is suitable to obtain physiological muscle trajectory. A FE glenohumeral joint model was developed based on medical imaging. Moment arms were computed and compared to literature and MRI-based estimation. Our FE model produces moment arms consistent with the literature and with MRI data (max 17 mm differences). The inferior and superior fibres of a same muscle can have opposite action; predictions of moment arms are sensitive to muscle insertion (up to 20 mm variation).
In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis functions within GMsFEM ...framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is appropriately chosen. We would like to show a mesh-dependent convergence with a minimal number of basis functions. Our construction starts with an auxiliary multiscale space by solving local spectral problems. In auxiliary multiscale space, we select the basis functions that correspond to small (contrast-dependent) eigenvalues. These basis functions represent the channels (high-contrast features that connect the boundaries of the coarse block). Using the auxiliary space, we propose a constraint energy minimization to construct multiscale spaces. The minimization is performed in the oversampling domain, which is larger than the target coarse block. The constraints allow handling non-decaying components of the local minimizers. If the auxiliary space is correctly chosen, we show that the convergence rate is independent of the contrast (because the basis representing the channels are included in the auxiliary space) and is proportional to the coarse-mesh size (because the constraints handle non-decaying components of the local minimizers). The oversampling size weakly depends on the contrast as our analysis shows. The convergence theorem requires that channels are not aligned with the coarse edges, which hold in many applications, where the channels are oblique with respect to the coarse-mesh geometry. The numerical results confirm our theoretical results. In particular, we show that if the oversampling domain size is not sufficiently large, the errors are large. To remove the contrast-dependence of the oversampling size, we propose a modified construction for basis functions and present numerical results and the analysis.
Numerical solution of the problem for Poisson’s equation with the use of Daubechies wavelet discrete continual finite element method (specific version of wavelet-based discrete-continual finite ...element method) is under consideration in the distinctive paper. The operational initial continual and discrete-continual formulations of the problem are given, several aspects of finite element approximation are considered. Some information about the numerical implementation and an example of analysis are presented.
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite ...element method and mortar methods. Our formulation is novel in that it employs the normal fluxes as the mortar variable within the mixed finite element framework, resulting in a formulation that couples the flow in the fractures with the surrounding domain with a strong notion of mass conservation. The proposed discretization handles complex, nonmatching grids and allows for fracture intersections and termination in a natural way, as well as spatially varying apertures. The discretization is applicable to both two and three spatial dimensions. A priori analysis shows the method to be optimally convergent with respect to the chosen mixed finite element spaces, which is supported by numerical examples.
This article presents a novel multiobjective system level optimization method to achieve the best performance of switched reluctance motor (SRM) drive systems. First, the multiobjective optimization ...problem for the SRM drive systems is defined. Then, all parameters of the drive systems, including the motor level and control level, are divided into three subspaces according to their influences on the objectives. Finally, the optimization of each subspace is performed sequentially until a convergence criterion is met. Then, the optimal solution can be chosen from the Pareto solutions according to a selection criterion. Meanwhile, the sensitivity analysis, the approximate models, and the genetic algorithm are employed to reduce the computation cost. To verify the effectiveness of the proposed method, an SRM drive system with a segmented-rotor SRM (SSRM) and the angle position control method is investigated. This is a high-dimensional system level optimization problem with ten parameters. The finite-element model (FEM) results are verified by the experiment results. The optimal solution has been listed and verified by the FEM. From the discussion, it can be found that the proposed optimization method is efficient and optimized SSRM drive system has high efficiency and low torque ripple.
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