Conventional Finite Element Method Research Articles

Dynamic analysis of the three-phase magnetic-electric-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Abstract In this work, a carefully designed enriched finite element method (EFEM) is presented to improve the solution accuracy of the conventional FEM in analyzing the dynamic behaviors of the magnetic-electric-elastic (MEE) composite structures which are frequently used in designing various smart and intelligent devices. In formulating the proper EFEM with ideal numerical performance, different enrichment functions are considered and the corresponding solution quality of different versions of the EFEM are compared and examined in great detail. When the Lagrange polynomial basis functions together with the harmonic trigonometric functions are used as the enrichment functions, the obtained EFEM shows extremely powerful and ideal numerical performance, which are obviously better than the other versions of EFEM and the conventional FEM, in studying the free vibration and harmonic frequency responses of the MEE structures. The nearly exact numerical solutions for three-phase physical fields of MEE structures can be generated by the proposed EFEM even if very coarse mesh patterns are used. Intensive numerical studies are conducted to confirm and verify the excellent properties of the proposed EFEM in performing dynamic analysis of the MEE structures.

Boundary element method for bending-extension coupling shear deformable laminated composite plates with multiple stiffeners

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations.

On effect of residual stress on fracture behavior of mandibular reconstruction plates

Titanium reconstruction plates are often used to bridge mandibulectomy defects in load bearing scenarios when bone grafts are not well integrated to the host bone. The residual stress within a standard reconstruction plate is generated when being bent and installed to adapt to a patient-specific anatomical contour and it may have a detrimental effect on the structural stability and reliability of the reconstruction system. This study aimed to evaluate the impact of residual stress on the mechanical strength of the reconstructed mandibular system by utilizing both conventional finite element method (FEM) and eXtended Finite Element Method (XFEM). The mechanical stresses introduced by plate pre-bending and screw tightening were first modeled computationally and the residual stress data induced by the surgical procedure was incorporated to the deformed reconstruction plate for the subsequent biomechanical evaluation. Static and cyclic loading conditions were then imposed on the mandibular plate models to further investigate two common failure types, namely overloading fracture and fatigue fracture. It is revealed that the residual stress could considerably increase the susceptibility of plate fracture. The simulation results demonstrate that the pre-stresses induced by screw tightening are more substantial than that from plate bending during the surgical procedure. The finding is of important clinical implications for surgeons who are commonly involved in selecting and preparing different forms of fixation plates for mandibular reconstruction. This study helps elucidate the key factors contributing on the failure of reconstruction plates and guide the development of more robust and durable mandibular reconstruction systems.

Theoretical modeling and experimental investigation of in-phase resonant MEMS mirrors with cascaded structures

This paper proposes an efficient nonlinear one-dimensional (1D) compact mass-damper-spring model to predict the dynamic response of electrostatic resonant micro-electro-mechanical system (MEMS) mirrors with cascaded structures. The time-dependent damping moment due to viscous shear and pressure drag is computed using semi-empirical analytical equations for comb-drive structures and device frames. Nonlinear electrostatic force induced by the comb drives is efficiently acquired based on the hybrid method. The optimized device is fabricated using MEMS fabrication processes based on a 4-inch silicon-on-insulator wafer. The proposed compact model with the measured key parameters from the fabricated device shows excellent capability to accurately predict nonlinear dynamic responses of the fabricated device, including parametric excitation and hysteretic frequency response, with an average error of less than 5%. In particular, our 1D model is three orders of magnitude faster than the conventional finite element method model (0.8 s versus 1 h), enabling efficient system-level optimization of the critical design parameters. Based on the parametric study, electrode gap distance and torsion spring width are found to be two critical design parameters and dimensional analysis is conducted for design optimization with scan angle enhancing from 16.8° to 24° compared with the first design.

Artificial intelligence-based surrogate model for computation of the electric field of high voltage transmission line ceramic insulator with corona ring

Purpose The ionization of the air surrounding the phase conductor in high-voltage transmission lines results in a phenomenon known as the Corona effect. To avoid this, Corona rings are used to dampen the electric field imposed on the insulator. The purpose of this study is to present a fast and intelligent surrogate model for determination of the electric field imposed on the surface of a 120 kV composite insulator, in presence of the Corona ring. Design/methodology/approach Usually, the structural design parameters of the Corona ring are selected through an optimization procedure combined with some numerical simulations such as finite element method (FEM). These methods are slow and computationally expensive and thus, extremely reducing the speed of optimization problems. In this paper, a novel surrogate model was proposed that could calculate the maximum electric field imposed on a ceramic insulator in a 120 kV line. The surrogate model was created based on the different scenarios of height, radius and inner radius of the Corona ring, as the inputs of the model, while the maximum electric field on the body of the insulator was considered as the output. Findings The proposed model was based on artificial intelligence techniques that have high accuracy and low computational time. Three methods were used here to develop the AI-based surrogate model, namely, Cascade forward neural network (CFNN), support vector regression and K-nearest neighbors regression. The results indicated that the CFNN has the highest accuracy among these methods with 99.81% R-squared and only 0.045468 root mean squared error while the testing time is less than 10 ms. Originality/value To the best of the authors’ knowledge, for the first time, a surrogate method is proposed for the prediction of the maximum electric field imposed on the high voltage insulators in the presence Corona ring which is faster than any conventional finite element method.

Implicit direct time integration of the heat conduction problem in the Method of Matched Sections

The paper is devoted to further elaboration of the Method of Matched Sections as a new branch of finite element method in application to the transient 2D temperature problem. The main distinction of MMS from conventional FEM consist in that the conjugation is provided between the adjacent sections rather than in the nodes of the elements. Important feature is that method is based on approximate strong form solution of the governing differential equations called here as the Connection equations. It is assumed that for each small rectangular element the 2D problem can be considered as the combination of two 1D problems – one is x-dependent, and another is y-dependent. Each problem is characterized by two functions – the temperature, , and heat flux . In practical realization for rectangular finite elements the method is reduced to determination of eight unknowns for each element – two unknowns on each side, which are related by the Connection equations, and requirement of the temperature continuity at the center of element. Another salient feature of the paper is an implementation of the original implicit time integration scheme, where the time step became the parameter of shape function within the element, i.e. it determines the behavior of the Connection equations. This method was early proposed by first author for number of 1D problem, and here in first time it is applied for 2D problems. The number of tests for rectangular plate exhibits the remarkable properties of this “embedded” time integration scheme with respect to stability, accuracy, and absence of any restrictions as to increasing of the time step.

A Coupled Finite-Boundary Element Method for Efficient Dynamic Structure-Soil-Structure Interaction Modeling

This paper introduces an innovative approach to numerically model Structure–Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM–FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design.

Bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness

In this paper, the boundary-based finite element method (BFEM) is developed for the bending-extension coupling analysis of shear deformable laminated composite curved beams with non-uniform thickness. The curved beams are discretized into a series of uniform straight segments. Based upon the first order shear deformation theory and the reciprocal theorem of Betti and Rayleigh, the boundary integral equations (BIEs) associated with each beam segment are derived and expressed in explicit form. The fundamental solutions required in the BIEs are obtained explicitly from the associated Green’s function. Since no singular integrals, numerical integrations and function interpolations are involved in the BIEs, our proposed BFEM provides an exact solution for a straight beam with uniform thickness, and only one single element with two end nodes is required for our analysis. Even only an approximate solution is provided for a curved beam with non-uniform thickness, BFEM converges faster than the conventional finite element method, and the results are in well agreement with those obtained by the commercial finite element software. Through the illustrated numerical examples, its generality is shown by: (1) stacking sequence of laminates: symmetric or unsymmetric; (2) beam geometries: straight, stepped, or curvilinear with uniform or non-uniform thickness; (3) loading types: axial force, transverse force and/or bending moment; distributed or concentrated; and (4) supporting conditions: clamped, simply supported, or free; with or without internal supports.

A particle finite element method approach to model shear cutting of high-strength steel sheets

AbstractShear cutting introduces residual strains, notches and cracks, which negatively affects edge-formability. This is especially relevant for forming of high-strength sheets, where edge-cracking is a serious industrial problem. Numerical modelling of the shear cutting process can aid the understanding of the sheared edge damage and help preventing edge-cracking. However, modelling of the shear cutting process requires robust and accurate numerical tools that handle plasticity, large deformation and ductile failure. The use of conventional finite element methods (FEM) may give rise to distorted elements or loss of accuracy during re-meshing schemes, while mesh-free methods have tendencies of tensile instability or excessive computational cost. In this article, the authors propose the particle finite element method (PFEM) for modelling the shear cutting process of high-strength steel sheets, acquiring high accuracy results and overcoming the stated challenges associated with FEM. The article describe the implementation of a mixed axisymmetric formulation, with the novelty of adding a ductile damage- and failure model to account for material fracture in the shear-cutting process. The PFEM shear-cutting model was validated against experiments using varying process parameters to ensure the predictive capacity of the model. Likewise, a thorough sensitivity analysis of the numerical implementation was conducted. The results show that the PFEM model is able to predict the process forces and cut edge shapes over a wide range of cutting clearances, while efficiently handling the numerical challenges involved with large material deformation. It is thus concluded that the PFEM implementation is an accurate predictive tool for sheared edge damage assessment.

Structural Reliability and Optimization Using Differential Geometric Approaches

This study investigates how differential geometry ideas can be used to effectively carry out structural optimization and reliability analysis. Strong mathematical representations and methods for examining intricate surfaces and forms are provided by differential geometry. The basic ideas of differential geometry, such as tensors, manifolds, and curvature, are initially introduced in the work. Then, to account for ambiguities in the geometry, the probability theory in tangent spaces is developed. As a result, structural reliability can be determined using propagating uncertainty. To enable reliability-based design optimization, differential geometry representations are linked with optimization techniques. The proposed differential geometry-based approach is applied in a number of case studies to trusses, airplane wings, car bodies, and ship hulls. The outcomes show a significant increase in productivity and scalability compared to conventional finite element methods. The article offers new tools for dealing with uncertainty.

Free Vibration Analysis of Laminated Sandwich Plates Using Wavelet Finite Element Method

The accuracy of a wavelet depends on the choice of the mother wavelet adopted. The present work aims to predict the free vibration behavior of laminated sandwich plates using wavelet finite element (WFE). Different kinds of mother wavelets, namely, B-spline wavelet on the interval (BSWI), Gaussian, Haar, Daubechies 6 (db6), Biorthogonal 3.7 (bior3.7), Coiflet5 (coif5), Symlets (sym8), Morlet, Mexican hat (Mh), and Meyer mother wavelets, are employed in WFE for predicting the frequencies. Both symmetric and unsymmetric laminates are studied using the proposed approaches. A wide range of problems, including the influence of the geometric and material properties and end conditions on the free vibration behavior of the laminated sandwich plates, are solved. The effectiveness of the WFE over the conventional finite element method in terms of computational efficiency is discussed. In conclusion, BSWI-based WFE method (WFEM) is found to be the most accurate and computationally efficient in predicting the free vibration behavior of laminated sandwich plates. The accuracy of the WFEM depends widely on the type of mother wavelet adopted.

Modelling of grain size effects in progressive microforming using CPFEM

Progressive microforming is widely recognized as one of the most efficient and desirable methods of mass production in micromanufacturing arena. To predict the deformation behaviour and size effects of materials induced in progressive microforming, the finite element method (FEM) employed for modelling the microforming process needs to account for microstructure details and deformation/failure mechanisms of the materials. This led to the development of the novel crystal plasticity finite element method (CPFEM) and cohesive zone model (CZM). Previous research and application of CPFEM have been mainly limited to simple deformations such as uniaxial tension and compression, whereas the new method can provide physical insights into how the grain size affects the interplay between crystallographic slip and mechanical twinning in complex microforming, and further material deformation during sheet blanking. A case study was conducted to manufacture a hexagonal socket part using a three-step progressive microforming system, with the comparison between experiments and CPFEM simulations focusing on microstructure evolution, deformation load, and product quality. The CPFEM was found to be more reliable than the conventional FEM in predicting complex deformation, particularly in microstructure and texture evolution, dimensional accuracy and irregular geometries. Results showed that the total height of the part increases with the decreasing grain size, while the head diameter rises with grain size. Simulations successfully anticipated the distributions of dead metal zones and shear bands and identified hole and rollover geometries and corresponding grain size effects. In conclusion, this research facilitates the understanding of grain size effects on the deformation behaviour in progressive microforming and presents a novel approach and strategy for modelling, prediction, and product quality assurance in complex micro deformation and forming processes.

A 3D finite element spectral integral (FESI) method for acoustics

We present a novel hybrid method that integrates the spectral integral method (SIM) with finite element for pressure acoustics in an inhomogeneous medium surrounded by spherical or incomplete spherical surfaces. Our approach, called the finite element spectral integral (FESI) method, enables efficient calculations of the pressure field in near-field and far-field zones. It is more efficient than the conventional finite element method hybridized with the boundary element method (i.e., the FEBI method). Furthermore, we construct a symmetric coefficient matrix using the proposed symmetric coupling to speed up the FESI method. We demonstrate through several examples that our FESI method offers significantly improved efficiency and lower memory consumption compared to the FEM combined with the perfect matching layer method while achieving higher accuracy.

Performance of 2D-spectral finite element method in dynamic analysis of concrete gravity dams

This article presents a two-dimensional spectral finite element formulation for dynamic analysis of concrete gravity dams. Finite element method (FEM) is the one of the most extensively used analysis tools for solving problems of dynamic analysis of structures. However, it needs extensive computational resources and time for large structures, leading to the development of alternate computationally efficient modeling techniques over the past few decades. Some of these techniques are broadly termed as “Spectral Finite Element Methods” (SFEMs). Frequency domain-based SFEM (FDSFEM) and time domain-based SFEM (TDSFEM) are the most commonly used SFEMs found in the literature. This article provides a brief review of these methods identifying their key advantages and disadvantages; and explores the feasibility of applying such methods in the dynamic analysis of concrete gravity dams. Here, the TDSFEM has been used to perform the dynamic time history analysis of a concrete gravity dam due to its relative advantages over FDSFEM, which is challenging for irregular geometry and finite domain. Sensitivity analysis and convergence studies have been performed using 4-noded and 9-noded elements. The foundation of the dam has been modeled using two-dimensional infinite elements in both FEM and TDSFEM analysis, which is a novel application in the case of TDSFEM. This article quantifies the computational efficiency of TDSFEM over the conventional FEM by comparing the computation time in both methods and thus emphasizes the applicability of TDSFEM in dynamic analysis, especially in case of complex geometries and large two-dimensional structures (like concrete gravity dam). The results demonstrate the computational efficiency of TDSFEM over FEM when higher order elements are considered. Modal analysis and time history analysis results point that the use of higher order elements of TDSFEM can be a viable alternative to the use of the conventional FEM leading to significant saving in computational time with reasonable accuracy for dynamic analysis of large structures like concrete gravity dams.

Experimental and combined finite-discrete element simulation of the fracture behaviour of a rigid polyurethane foam

In the present paper, firstly the fracture toughness of a rigid polyurethane foam is experimentally measured by varying the specimen sizes and employing the Modified Two-Parameter Model. Then, such a testing campaign is numerically simulated by developing hybrid models, obtained by coupling a Discrete Element Method (that is, the Lattice Discrete Element Method) and a Finite Element Method (that is, the conventional FEM). Finally, in order to prove the robustness of the above hybrid LDE/FE models, a further experimental campaign, carried out on reinforced epoxy foams, is numerically simulated.

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Due to the heterogeneities in material properties of strongly-bonded multi-material composite structures, there exist singularities of the stress fields at the material interface as well as the interface corners on the bounding surfaces. The finite-element method is probably the only plausible option to analyze the stress around such interfaces between dissimilar materials subjected to combined thermo-mechanical loading. In this article, we propose a novel mathematical model for the computational analysis of coupled thermo-elastic fields with perfectly bonded interfaces of dissimilar isotropic/orthotropic composite-material structures. A scalar function of the spatial variables, namely, the displacement function, is used to integrate the temperature field and the associated displacement-function field to obtain two nonhomogeneous partial-differential equations of equilibrium that govern two thermo-mechanical sub-problems defined in terms of the appropriate conditions of orthogonal temperature gradients. For a specific temperature field, obtained as a steady-state solution of the given thermal problem, the two thermo-mechanical sub-problems are solved independently to obtain the full-field solution of the thermo-elastic problem using the method of superposition. As an alternative to the conventional computational approach, we employed a single variable semi-analytical method of solution to determine the thermo-mechanical response of the multi-material composite structures. The continuity of the temperature and the heat flux in the thermal field problem and the continuity of the displacement and the traction vectors are utilized in the elastic field problem to determine the appropriate algebraic equations suitable for nodal application at the interfaces as well as interface corners on the boundaries of the respective problems. The quantitative comparison of the present displacement-function solutions to several mixed-boundary-value problems with those obtained by the conventional finite-element method verifies the high accuracy and effectiveness of the present method. This computational model has potential applications in identifying near-interface high-stress locations as well as possible critical regions of the physical boundary of composite structures subjected to mixed modes of thermal and mechanical loadings.

Efficient 3D Frequency Semi-Airborne Electromagnetic Modeling Based on Domain Decomposition

Landslides are common geological hazards that often result in significant casualties and economic losses. Due to their occurrence in complex terrain areas, conventional geophysical techniques face challenges in early detection and warning of landslides. Semi-airborne electromagnetic (SAEM) technology, utilizing unmanned aerial platforms for rapid unmanned remote sensing, can overcome the influence of complex terrain and serve as an effective approach for landslide detection and monitoring. In response to the low computational efficiency of conventional semi-airborne EM 3D forward modeling, this study proposes an efficient forward modeling method. To handle arbitrarily complex topography and geologic structures, the unstructured tetrahedron mesh is adopted to discretize the earth. Based on the vector finite element formula, the Dual–Primal Finite Element Tearing and Interconnecting (FETI-DP) method is further applied to enhance modeling efficiency. It obtains a reduced order subsystem and avoids directly solving huge overall linear equations by converting the entirety problem into the interface problem. We check our algorithm by comparing it with 1D semi-analytical solutions and the conventional finite element method. The numerical experiments reveal that the FETI-DP method utilities less memory and exhibits higher computation efficiency than the conventional methods. Additionally, we compare the electromagnetic responses with the topography model and flat earth model. The comparison results indicate that the effect of topography cannot be ignored. Further, we analyze the characteristic of electromagnetic responses when the thickness of the aquifer changes in a landslide area. We demonstrate the effectiveness of the 3D SAEM method for landslide detection and monitoring.

Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization

AbstractUnfitted finite element methods (FEM) have attractive merits for problems with evolving or geometrically complex boundaries. Conventional unfitted FEMs incorporate penalty terms, parameters, or Lagrange multipliers to impose the Dirichlet boundary condition weakly. This to some extent increases computational complexity in implementation. In this article, we propose an unfitted generalized FEM (GFEM) for the Dirichlet problem, which is free from any penalty or stabilization. This is achieved by means of partition of unity frameworks of GFEM and designing a set of new enrichments for the Dirichlet boundary. The enrichments are divided into two groups: the one is used to impose the Dirichlet boundary condition strongly, and the other one serves as energy space of variational formulations. The shape functions in energy space vanish at the boundary so that standard variational formulae like those in the conventional fitted FEM can be applied, and thus the penalty and stabilization are not needed. The optimal convergence rate in the energy norm is proven rigorously. Numerical experiments and comparisons with other methods are executed to verify the theoretical result and effectiveness of the algorithm. The conditioning of new method is numerically shown to be of same order as that of the standard FEM.

The s-version finite element method for non-linear material problems

This study intended to extend the s-version of the finite element method (s-version FEM) to cope with elastic–plastic problems. Compared with the conventional FEM, the s-version FEM, which overlays a set of local mesh with fine element size representing irregular features over the conventional FE mesh with coarse element size, can considerably simplify issues in domain discretisation with fewer degrees of freedom and provide accurate numerical predictions. However, most applications of the s-version FEM were limited to elastic problems only, leaving its applications to elastic–plastic problems almost blank owing to insufficient instructions on stress update when plasticity sets in. To address these issues, detailed instructions and formulations to cope with plasticity problems with the s-version FEM were presented for its first time. The recursive element subdivision technique was implemented to generalise its application where local elements intersect with global element edges. A 3D stress concentration problem with linear/non-linear material properties was analysed; their numerical results were compared with the exact solutions and those obtained from the conventional FEM with very fine elements. The comparison highlights the flexibility of the s-version FEM in domain discretisation and its superior accuracy in numerical calculations, thereby exhibiting high potential applications in structural integrity assessment with complex structures, geometric defects, and material non-linearity.

Quasi-3D Model for Lateral Resonances on Homogeneous BAW Resonators.

Lateral modes are responsible for the in-band spurious resonances that appear on BAW resonators, degrading the in-band filter response. In this work, a fast computational method based on the transmission line matrix (TLM) method is employed to model the lateral resonances of BAW resonators. Using the precomputed dispersion curves of Lamb waves and an equivalent characteristic impedance for the TE1 mode, a network of transmission lines is used to calculate the magnitude of field distributions on the electrodes. These characteristics are specific to the stack layer configuration. The model's implementation is based on nodal Y matrices, from which particle displacement profiles are coupled to the electric domain via piezoelectric constitutive relations. Consequently, the input impedance of the resonator is obtained. The model exhibits strong agreement with FEM simulations of FBARs and SMRs, and with measurements of several SMRs. The proposed model can provide accurate predictions of resonator input impedance, which is around 200 times faster than conventional FEM.