Finite Elements in Analysis and Design最新文献

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry, whereas a fine distribution of overlapping nodes is used to perform higher order approximations via the improved element-free Galerkin (IEFG) technique in regions demanding more computational accuracy. The method relies on keeping the FEM-based results in those regions where low order of approximation is enough to provide the required accuracy, i.e. outside the region where the solution will be enriched via the IEFG technique. The overlapping domains perform an iterative transfer of kinematics information through well-defined immersed boundaries, and a detailed explanation on this regard is also presented in this communication. The Ov-IEFG-FEM is used in a set of increasingly complex linear elasticity problems, and the outcomes demonstrate the suitability and reliability of this technique to solve such problems in an accurate and remarkably simple manner.

Metal-ceramic composites by their nature have thermal residual stresses at the micro-level, which can compromise the integrity of structural elements made from these materials. The evaluation of thermal residual stresses is therefore of continuing research interest both experimentally and by modeling. In this study, two functionally graded aluminum alloy matrix composites, AlSi12/Al₂O₃ and AlSi12/SiC, each consisting of three composite layers with a stepwise gradient of ceramic content (10, 20, 30 vol%), were produced by powder metallurgy. Thermal residual stresses in the AlSi12 matrix and the ceramic reinforcement of the ungraded and graded composites were measured by neutron diffraction. Based on the X-ray micro-computed tomography (micro-XCT) images of the actual microstructure, a series of finite element models were developed to simulate the thermal residual stresses in the AlSi12 matrix and the reinforcing ceramics Al₂O₃ and SiC. The accuracy of the numerical predictions is high for all cases considered, with a difference of less than 5 % from the neutron diffraction measurements. It is shown numerically and validated by neutron diffraction data that the average residual stresses in the graded AlSi12/Al₂O₃ and AlSi12/SiC composites are lower than in the corresponding ungraded composites, which may be advantageous for engineering applications.

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.

Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized using a variational multiscale FEM. A non-linear ANN correction term is then designed to be added to the FEM algebraic matrix system and produce accurate solutions when solving elastodynamics on coarse meshes. As a case study we consider acoustic black holes (ABHs) on structural elements with high aspect ratios such as beams and plates. ABHs are traps for flexural waves based on reducing the structural thickness according to a power-law profile at the end of a beam, or within a two-dimensional circular indentation in a plate. For the ABH to function properly, the thickness at the termination/center must be very small, which demands very fine computational meshes. The proposed strategy combining the stabilized FEM with the ANN correction allows us to accurately simulate the response of ABHs on coarse meshes for values of the ABH order and residual thickness outside the training test, as well as for different excitation frequencies.

A generalized finite element beam with an embedded rotation discontinuity coupled with a 3D macroelement is proposed to assess, till complete failure (no stress transfer), the vulnerability of symmetrically reinforced concrete frame structures subjected to static (monotonic, cyclic) or dynamic loading. The beam follows the Timoshenko beam theory and its sectional behavior is described in terms of generalized forces and generalized strains. The beam response up to the peak is described by a macroelement, based on plasticity theory, that adopts a 3D failure criterion expressed in terms of axial force, shear force and bending moment. The Embedded Finite Element Method is then adopted to reproduce bending dominated failure, with a global cohesive model that links the cohesive moment to a rotational jump. The formulation allows for remedy of localization phenomena and significant reduction of the necessary computational time. The performance of the proposed simplified strategy is illustrated by comparison with experimental results.

To obtain the displacement field of stiffened panel structures is very important for the online monitoring of aircraft or aerospace vehicles, etc. New inverse beam-shell elements are proposed in this study for the full-field displacement reconstruction of stiffened panels via strain measured by shell parts and rib parts simultaneously. The shell and rib parts in the stiffened panel are modeled by inverse shell and beam elements respectively constructed by Mindlin's plate theory and Timoshenko beam theory. To avoid the shear locking, a new inverse beam element with a virtual middle node is introduced. Constraints between the inverse shell and beam elements are given to guarantee the consistency of deformation and two typical inverse beam-shell elements are proposed. A sub-area division scheme is introduced which enables the proposed inverse elements for reconstructing the displacement field of 3D structures composed of multiple stiffened panels. Two numerical examples including a cantilever stiffened panel and a two-edge clamped 3D stiffened panel are given to demonstrate the effectiveness of the newly proposed inverse beam-shell element and the sub-area division scheme. An element-selection scheme for the arrangement of strain gauges is also proposed to reduce the measurement data used. Results show the new inverse beam-shell elements can reconstruct displacement fields accurately and the sub-area division scheme introduced guarantees the accuracy of the reconstructed displacement fields of 3D panels even when a relatively small number of strain gauges are used.

Conjugate heat transfer (CHT) problem of flow around a fixed cylinder is examined by using a high-order method which is based on the hybridizable discontinuous Galerkin (HDG) method. The present numerical method based on HDG discretization produces a system of equations in which the energy equation of fluid is coupled with that of solid while the continuity of heat-flux at the fluid-solid interface is automatically satisfied. We Investigate the effect of the conductivity ratio on the temperature distribution inside the cylinder and more importantly, the constraint of heat-flux continuity at the fluid-solid interface. The present high-order solutions are compared with low-order solutions by finite volume method of ANSYS, especially in terms of the constraint of heat-flux continuity at the interface. We show that the present high-order method provides accurate solutions and satisfies the constraint of heat-flux continuity better than ANSYS even with the use of a coarse grid. Furthermore, we have derived a numerical correlation between the Nusselt and the Reynolds number by using the fact that the surface temperature of the cylinder is nearly constant when conductivity ratio is larger than order of hundred. The proposed numerical correlation was found to be close to that from the exiting experiment.

This study presents a multiobjective optimization framework that integrates Artificial Neural Network (ANN) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for the optimization of rolling process parameters of tube-to-tubesheet joint (TTT-joint). During the rolling process, both beneficial contact pressure and detrimental tensile residual stress are generated within the joint. The primary objective of this framework is to minimize the tensile residual stress while maximizing the contact pressure in the TTT-joint. To achieve this, a backpropagation ANN model is trained to rapidly estimate the residual stress and contact pressure for various sets of rolling process parameters. For training purposes, a series of nonlinear elastoplastic finite element (FE) simulations are performed to generate the input database for the neural network. A detailed parametric study is performed based on the axisymmetric FE model of the TTT-joint. The trained neural network is then incorporated into the NSGA-II optimization algorithm to find the fitness function and optimized process parameters. The contact pressure and residual stress predicted by the proposed ANN-NSGA-II framework are validated by finite element analysis (FEA) using the optimized parameters. The present analysis established that the proposed methodology can be applied in practical engineering problems to obtain the process parameters that yield the maximum contact pressure and minimum tensile residual stress in the TTT-joint.

When the finite element method (FEM) is adopted for studying strain localization problems, the mesh dependence phenomenon often ensues. The occurrence of mesh dependency will reduce the reliability of FEM simulations, so it is still worth studying. Herein, a constitutive model with decent mesh stability named the multiscale Cosserat (MC) model which contains higher-order rotation variables based on the conventional Cosserat (CC) theory, was introduced. The theory derivation indicates that the MC model has an extra internal length scale vector D_q that can consider the microscopic geometrical characteristics of the simulated material and can easily regress to the conventional Cosserat model when D_q = 0. After revisiting the mesh dependence problem through numerical simulations of plane strain compression tests, the mechanisms and advantages of the CC and MC models in solving the mesh dependence problem were discussed. The analysis demonstrated that the CC theory can alleviate the mesh dependence problem but cannot eliminate it; when the divergence of the computation occurs, due to a stricter accuracy requirement for convergence, the computation result of the MC model tends to stabilize along with the refinement of the elements. The mesh advantage of the MC model is influenced by both the length scales l and D_q. This study can provide new insight into understanding the mesh dependence problem, and the MC model introduced here is a potential model for comprehensively eliminating the influence of mesh dependence problems.

In this study, the vibration stability (i.e., static divergence) and critical velocity of fluid-conveying, ring-stiffened, truncated conical shells are investigated under various boundary conditions. The shell is characterized using Sanders’ theory, while the fluid is modeled using a velocity potential approach with the impermeability condition at the fluid-shell interface. Using linear superposition, the natural frequencies corresponding to each flow velocity are determined by satisfying the dynamic characteristic equation and boundary conditions. Critical velocities are identified where the natural frequencies vanish, indicating static divergence. Parametric studies are conducted to investigate the effect of ring stiffeners on the critical velocities with respect to the semi-cone angle, number of rings, and boundary conditions. The proposed model is validated through comparison with published data. It is found that the rings significantly affect the stability of the cone under different boundary conditions. Instability in stiffened shells occurs at higher critical fluid velocities than in unstiffened shells across all boundary conditions. An increase in the vertex angle leads to a decrease in critical flow discharge.