FEM Results Research Articles

A study on evaluation method of local pipe wall thinning based on DC potential difference measurement

In this study, a simple method to evaluate the local pipe wall thinning by using the DC potential difference method was examined. The pipe has outer diameter D and thickness t0. The local inner-wall thinning is modeled as a back wall slot having arc-shape cross section of width 2w and depth b. The constant DC current is applied to the pipe through two probes, and the distribution of potential difference between current input and output probes is measured. The potential differences measured before and after thinning are represented as V0 and V1, respectively. The thinning depth b/t0 is evaluated from the maximum value of V1/V0. Three-dimensional finite element method was used to analyze the relation between thinning size and potential difference for various cases. As a result, it was shown that the relation between b/t0 and V1/V0 is affected by w/D. The calibration equation between b/t0 and V1/V0 was obtained by approximating FEM results, and its validity was shown by numerical experiments.

Discrete Element Simulations of Ice Load and Mooring Force on Moored Structure in Level Ice

Moored structures are suitable for operations in ice-covered regions owing to their security and efficiency. This paper aims to present a new method for simulating the ice load and mooring force on the moored structure during ice-structure interaction with a spherical discrete element method (DEM). In this method, the level ice and mooring lines consist of bonded sphere elements arranged in different patterns. The level ice model has been widely validated in simulation of the ice load of fixed structures. In the mooring line simulation, a string of spherical elements was jointed with the parallel bond model to simulate the chains or cable structure. The accuracy of the mooring line model was proved by comparing the numerical results with the nonlinear FEM results and model towing experiment results. The motion of the structure was calculated in the quaternion method, considering the ice load, mooring force, and hydrodynamic force. The hydrodynamic force comprised wave-making damping, current drag, and buoyancy force. Based on the proposed model, the interaction of a semi-submersible structure with level ice was simulated, and the effect of ice thickness on the ice load was analyzed. The numerical results show that the DEM method is suitable to simulate the ice load and mooring force on moored floating structures.

Selected aspects of a cold forging process for hollow balls

This paper presents the results of a study investigating a cold forging process for producing hollow balls with different wall thicknesses. The study was performed by FEM numerical modelling, which made it possible to obtain a wide spectrum of results. For the analysis of FEM results obtained for problematic cases (shape defects in forged balls), novel hypotheses for results interpretation are proposed. The FEM numerical model and hypotheses are then verified via experimental testing, and selected theoretical results are compared with experimental findings. Finally, obtained results are discussed (e.g. the effect of billet dimensions on forging conditions, wall thickness and hole size), a method for FEM results interpretation is presented, and design-related solutions ensuring the production of defect-free hollow balls are proposed.

Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory

The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.

Multiple Impact Damage in GLARE Laminates: Experiments and Simulations.

Experiments and finite element simulations for multiple impact were performed on GLARE 5-2/1 and aluminum 2024-T3. Experiments were conducted on aluminum 2024-T3 and GLARE 5-2/1 at diverse impact energies to produce BVID (barely visible impact damage) and CVID (clearly visible impact damage). The finite element model was developed for multiple impact analysis using ABAQUS software and was confirmed by comparing the finite element analysis outcomes with experimental results. The two- and three-dimensional failure criteria model was applied to predict multiple impact behavior such as load-time history, maximum deflection-impact energy history, and damage progression. In addition, a user subroutine VUMAT was created to represent a three-dimensional progressive failure and was linked with ABAQUS. FEM results showed good agreement with experimental data.

Ultimate Axial Load Prediction Model for X65 Pipeline with Cracked Welding Joint Based on the Failure Assessment Diagram Method

Crack defects in the girth welds of pipelines have become an important factor affecting the safe operation of in-service oil pipelines. Therefore, it is necessary to analyze the factors affecting the safe operation of pipelines and determine the ultimate load during pipeline operation. Based on the failure assessment diagram (FAD) method described in the BS 7910 standard, the key factors affecting the evaluation results of the suitability of X65 pipeline girth welds are analyzed, and the effects of crack size, pipe geometry, and material properties on the evaluation results are investigated. The results indicate that the crack depth is more crucial to the safe operation of the pipeline than the crack length. While the effect of wall thickness is not significant, the misalignment can seriously aggravate the stress concentration. In general, the higher the yield ratio and tensile strength of the pipe material, the more dangerous the condition at the weld. The ultimate axial load that a crack-containing girth weld can withstand under different combinations of the above factors was determined. Furthermore, a data driven model via the optimized support vector regression method for the ultimate axial load of the X65 pipe was developed for engineering application, and the comparison results between the FEM results and the predicted results proved its accuracy and reliability.

Improvement of Shape Error for Slender Parts in Cylindrical Traverse Grinding by Part-Deformation Modelling and Compensation

Achieving geometrical accuracy in cylindrical traverse grinding for high-aspect slender parts is still a challenge due to the flexibility of the workpiece and, therefore, the resulting shape error. This causes a bottleneck in production due to the number of spark-out strokes that must be programmed to achieve the expected dimensional and geometrical tolerances. This study presents an experimental validation of a shape-error prediction model in which a distributed load, corresponding to the grinding wheel width, is included, and allows inclusion of the effect of steady rests. Headstock and tailstock stiffness must be considered and a procedure to obtain their values is presented. Validation of the model was performed both theoretically (by comparing with FEM results) and experimentally (by comparing with the deformation profile of the real workpiece shape), obtaining differences below 5%. Having determined the shape error by monitoring the normal grinding force, a solution was presented to correct it, based on a cross-motion of the grinding wheel during traverse strokes, thus decreasing non-productive spark-out strokes. Due to its simplicity (based on the shape-error prediction model and normal grinding force monitoring), this was easily automatable. The corrective compensation cycle gave promising results with a decrease of 77% in the shape error of the ground part, and improvement in geometrically measured parameters, such as cylindricity and straightness.

Time-domain elasto-dynamic model of a transversely isotropic, layered road structure system with rigid substratum under a FWD load

In this paper, the time-domain elasto-dynamic model of a transversely isotropic, layered road structure system resting on rigid bedrock under a falling weight deflectometer (FWD) load is proposed by using the Laplace-Hankel transformation, and developing an improved propagator matrix method (PMM) with less calculation cost, higher calculation accuracy and better numerical stability. The improved model greatly avoids the problem of data overflow and maintains the computational efficiency of PMM. The present model is then verified by comparing with the corresponding FEM results. A parametric analysis is finally performed to discuss the effects of material anisotropy and rigid substratum on dynamic response of a road system, which is meaningful for design and practice of road engineering with modulus back-calculation.

Analytical Solution of Composite Curved I-Beam considering Tangential Slip under Uniform Distributed Load

An analytical solution of composite curved I-beam considering the partial interaction in tangential direction under uniform distributed load is obtained. Based on the Vlasov curved beam theory, the global balance condition of the problem has been obtained by means of the principle of virtual work; integrating this by parts, the governing system of differential equations and corresponding boundary conditions have been determined. Analytical expressions for the composite beam considering the partial interaction have been developed. In order to verify the validity and the accuracy of this study, the analytical solutions are presented and compared with other three FEM results using the space beam element and the shell element. The deflection and the tangential slip of the composite curved I-beam are investigated.

Mechanical properties characterization and zero Poisson’s ratio design for perforated auxetic metamaterial by computational homogenized method

Metamaterial with elliptical perforations is characterized by a distinctive computational homogenized method. Two kinds of periodic displacement constraints representing tension and shear deformations, respectively, are applied to the unit cell. Then, the relationship of the undetermined displacement constraints in the micromechanical models and the assumed stress conditions in the equivalent orthotropic medium is derived to determine the effective properties. The method is validated by comparing to the experimental and FEM results. Next, the dependence of effective properties on microstructure parameters and base material composition is investigated. Correspondingly, the zero Poisson’s ratio design criterion is formulated to guide the metamaterial design.

Prediction of mechanical solutions for a laminated LCEs system fusing an analytical model and neural networks

This paper presents a convenient and efficient method to predict the mechanical solutions of a laminated Liquid Crystal Elastomers (LCEs) system subjected to combined thermo-mechanical load, based on a back propagation (BP) neural network which is trained by machine learning from a database established by analytical solutions. Firstly, the general solutions of temperature, displacement, and stress of any single layer in the LCEs system are obtained by solving the two-dimensional (2D) governing equations of both heat conduction and thermoelasticity. Then, the unknown coefficients in above general solutions are determined by a transfer-matrix method based on the continuity condition at the interface of adjacent layers and the combined thermo-mechanical loads condition at the surface of the LCEs system. The formula derivation and calculator program are verified through convergence studies and comparisons with FEM results. Finally, a database with displacements of LCEs system in a temperature field subjected to 561 sets of mechanical loads is established based on the presented analytical model. The BP neural network based on above database is further applied to establish the relationship between deformation and mechanical load to predict the elastic deformation of the LCEs system in a temperature field subjected to a mechanical load. Moreover, the BP network can also inverse the coefficients of mechanical load which induces the specific deformation in a temperature field. The numerical examples show that: (1) The deformation of a laminated LCEs system due to thermal load is limited within the range of human temperature changes from 36 °C to 40 °C. (2) The thickness of the LCE is a sensitive parameter on the deformation at the bottom surface of the system. (3) The accuracy of predicted displacements induced by the thermo-mechanical load and the inversed mechanical load based on deformation of the LCEs system in a temperature field using BP neural network reaches 99.6% and 98.5% respectively.

Analytical method of the modal damping ratio of the beam with distributed dissipative oscillators and application in broadband vibration mitigation

Distributed dissipative oscillators are considered effective measures to broaden the vibration mitigation bandwidth of structures. However, the existing calculation methods are mainly based on parameter analysis, which is not convenient for engineering applications. Modal damping ratio can be used to evaluate the frequency band and degree of vibration attenuation quickly. Therefore, the explicit analytical formulas of modal damping ratio for the beam distributed with single-frequency and dual-frequency oscillators are derived and verified by comparing with FEM results. And the influence of mode order, boundary conditions, the mass ratio, and frequency ratio of the oscillators on modal damping ratio is also discussed. As an application of the presented equations, the optimized frequencies of single-frequency or dual-frequency oscillators satisfying the Minimax optimization (maximize the minimum damping in a target frequency band) are obtained. The frequency response of the beam with optimized oscillators is compared with modal damping ratio curves to discuss the influence of mass ratio and loss factor on vibration suppression and the adaptability of modal damping to design. The results show that the presented formulas have satisfied accuracy and can be used for broadband mitigation design.

Analysis of residual plastic deformation of blanked sheets out of automotive aluminium alloys through hardness map

Reducing overall vehicle weight is essential to reduce fuel consumption and pollutant emission and to improve noise, vibration, and harshness (NVH) performances. The substitution with lighter alloys can involve the grand majority of vehicle components, depending on the market sector. In several applications, e.g., chassis, pulleys, and viscodampers, metal sheets are formed in several steps, each of whom work-hardens the material reducing the available residual plasticity. Typically, the process is designed via FEM, whose results are affected by the initial conditions, often neglected, and is performed on pre-processed materials from suppliers. In this regard, correctly simulating the first step of the process is critical. However, the related initial conditions, in terms of residual stress and strain induced by former preliminary operations, are often neglected. This work proposes a quick and economical experimental procedure based on a hardness map to estimate initial conditions and to validate FEM results. The procedure allows evaluating the material’s residual plasticity, which is necessary to process engineers to design following manufacturing steps. The approach is demonstrated on an industrially relevant case study, i.e., the blanking of an AA 5754, in use for water pump pulleys.

Structural analysis method of a pontoon-separated floating bridge connected by elastic hinges

ABSTRACT An analytical method that can be generally applied to structural analysis of a pontoon-separated floating bridge connected by elastic hinges is proposed based on elastic foundation beam theory and Euler beam theory. This method can solve the displacement, rotation angle, bending moment and shearing force of a pontoon-separated floating bridge under vertical static loads. Validation of the method is established through comparing with the numerical results of AQWA software and FEM. Simultaneously, the main response characteristics of a pontoon-separated floating bridge and a floating pier are further investigated. The results reveal that the rotation stiffness of elastic hinges has a significant influence on the responses of the pontoon-separated floating bridge. Besides, the elastic deformation of the floating bridge can be ignored when the rotation stiffness of hinge is relatively small, while it needs to be considered seriously when the rotation stiffness of hinges reaches a certain value.

Dynamic coupling vibration of rotating shaft–disc–blade system — Modeling, mechanism analysis and numerical study

This study aims at revealing the coupling vibration mechanism of RSDB system. First, a comprehensive coupling dynamic model of RSDB system including the shaft bending, shaft torsion, blade bending, and blade radial deformation is formulated based on continuum beam theory and Lagrange equation. The validity of the proposed dynamic model is verified through a comparison with FEM and experimental results. Second, the general coupling mechanism of RSDB system is theoretically interpreted based on the proposed analytical coupling vibration model, which indicates that the blade vibration and shaft vibration, especially the shaft torsion vibration and blade bending vibration, may affects each other significantly. At last, the steady-state coupling vibration responses and the effects of structure parameters on the coupling vibration of RSDB system are comparatively investigated through numerical investigations. The comparative results suggest that the blade setting angle, blade–blade coupling stiffness, and the disc location on shaft will greatly affect the coupling vibrations. It worth more attention that the general coupling vibration mechanism obtained by analytical analysis and the results obtained by numerical study can be cross-verified by each other.

Analysis and design of axial inductive displacement sensor

An axial inductive displacement sensor, which can be fixed on radial direction to measure axial displacement of the suspended rotor, is proposed in this paper. Based on Schwarz-Christoffel transformation, 3D inductance of the proposed sensor is calculated. The novel approach for 3D inductance calculation is compared with 3D FEM results, showing the feasibility for practical applications. Static and dynamic characteristics are evaluated on a magnetic bearing platform. Sensitivity and linearity are 2.63 V/mm and 0.46%, respectively. Static noise result shows that the proposed sensor can reach a resolution of 5 μm. Dynamic characteristics tests, including vibrating and shocking experiments show that the displacement detection capability of the proposed sensor is similar to that of an eddy current sensor, showing the potential of the proposed sensor used in other fields where eddy current sensors have already be applied.

A combined experimental/numerical study on deformation sensing of sandwich structures through inverse analysis of pre-extrapolated strain measurements

Real-time reconstruction of displacement field from a network of discrete strain sensors is referred to as “shape (deformation) sensing” for which inverse finite element method (iFEM) has been extensively studied and proven to be an efficient, robust, and accurate algorithm. In this study, practical shape-sensing capability of an enhanced iFEM formulation, which utilizes the kinematics of refined zigzag theory (RZT) as its baseline, is numerically and experimentally investigated for moderately thick sandwich plates/shells. To this end, a novel four-node inverse-shell element (iRZT4) is developed and implemented to discretize the governing equations of the iFEM-RZT formulation. Moreover, the iFEM-RZT approach is coupled with a polynomial-based strain pre-extrapolation technique to achieve a highly precise prediction for numerical and experimental case studies using different sensor deployment strategies. Various test cases namely stiffened plate and curved sandwich shells subjected to bending loads, and a wing-shaped sandwich panel exposed to torsional loading condition are solved to evaluate the performance of the iRZT4 element. For these problems, the results of iFEM-RZT analysis with/without ‘a priori’ smoothing of experimental strain data are compared with high-fidelity FEM reference solutions as well as the results of the classical iFEM formulation. In addition, through-the-thickness full-field displacement maps obtained from digital image correlation (DIC) are used to verify the iFEM and FEM results. These comparisons reveal that using a sparse sensor placement model for an iRZT4 discretization paired with the polynomial smoothing approach leads to the most precise, efficient, and reliable deformation reconstruction for moderately thick sandwich structures, among other strategies.

Analytical approach to the stepped multi-span rotor-bearing system with isotropic elastic boundary conditions

This paper strives to derive the analytical solutions for the dynamic analysis of stepped multi-span rotor system, where the rotating shaft's internal damping effect is also considered. Specifically, the steady-state whirl analysis and free vibration analysis is given herein. For the steady-state whirl analysis, firstly, the stepped shaft is spilt to several uniform segments and their governing equations are established by Hamilton principle. Subsequently, by applying variable separation method and Laplace transform method to each segment's governing equation, their steady-state responses in terms of determinate interpolation functions multiplied by unknown boundary constants are derived. Then based on the transfer matrix method, each segment's boundary constants are determined with consideration of the compatibility conditions of each two adjacent segments and the end boundary conditions. For the free vibration analysis, one only need to remove the forced term in the steady-state form of transfer matrix and the rotor's characteristic equation will be obtained. Through the theoretical derivation, it is found that this analytical approach can be generalized to any isotropic elastic boundary conditions. To validate the proposed method, two case studies are proposed, where the finite element method is used as benchmark method. For the first one, the influence of internal damping on a uniform rotor's damped whirl characteristics and its stability is analyzed. The damped whirl characteristics analysis reveals that viscous internal damping result in the destabilization of forward modes as long as the spinning speed becomes higher than the critical speed. This phenomenon is also demonstrated by the time responses analysis. For the second one, the dynamic responses of a two-span three steps rotor-bearing system with isotropic viscoelastic boundary conditions are determined. All of simulated results show a great agreement between analytical results and FEM results.

Finite element modeling and analysis of low symmetry piezoelectric shells for design of shear sensors

This work presents the development of a novel non-polynomial electromechanical shell theory for analysis of composite piezoelectric shell structures. The 2D shell theory is utilized to explore novel shear sensors made of low symmetry materials with simple patch geometries. Specifically, three configurations of patch sensors are analyzed: (i) torsional sensor operating in 36 mode, i.e., exhibiting in-plane shear coupling with electric field, (ii) transverse shear sensor operating in 35 mode exhibiting transverse shear coupling with electric field, and (iii) flexural sensor operating in 31 mode exhibiting bending stress-electric field coupling. To model these sensors, the electric potential and displacement fields are assumed to be inverse-hyperbolic functions of the thickness coordinate. A new computationally efficient C0 continuous deep shell finite element framework is developed starting from the principle of minimum potential energy, and additional continuity requirements are imposed through the use of penalty parameter approach. The results are verified by comparing with 3D FEM results. It is also observed that the inverse-hyperbolic theory has higher accuracy compared to the third-order polynomial theory for the same number of degrees of freedom. Parametric studies are subsequently performed to analyze the effect of geometric parameters such as thickness, radius of curvature of the shell, boundary conditions, thickness of the piezoelectric layer etc., on the sensor response of piezoelectric shell structures. It is observed that the response of these sensors is highly dependent on the boundary conditions, placement and thickness of the piezoelectric layer.

Longhu pagoda: Advanced numerical investigations for assessing performance at failure under horizontal loads

As an important historical building type for human beings, ancient masonry pagodas have key research significance. They are widely diffused in China, and they are tower-like masonry structures, usually massive and tall. This paper takes the Longhu pagoda as a case-study: it was built in 1342 CE, and it is the only masonry pagoda from the Yuan Dynasty. It is located in the Sichuan Province (China), it has a square plane, and the height is about 33 m. This construction severely suffered the so-called “2008 Sichuan Earthquake”. A full 3D model of the Longhu Pagoda has been obtained and subsequently meshed. The FE software Abaqus/CAE has been used for carrying out static analyses, pushover analyses and non-linear dynamic analyses. The material non-linearities have been taken into consideration employing the so-called Concrete Damage Plasticity (CDP) model available in Abaqus. Modal analyses have shown that FEM results and simplified cantilever model results may agree. Pushover analyses (POs) have been performed under different load conditions and along the four principal bending directions to estimate the global capacities and the corresponding collapse mechanisms. Non-linear dynamic analyses (NLDAs) allowed putting in evidence the accuracy of the results provided by the pushover analyses; besides, they gave helpful information about the crack propagation, confirming the damage reported on-site after the 2008 earthquake. The state of damage found and the related failure mechanisms have been deeply commented. Moreover, some sensitivity analyses have been performed to study the influence of some material parameters on the pushover results. Furthermore, two fictitious 3D models of the pagoda have been created by doubling and removing two floors to investigate the influence of the tower slenderness. The before mentioned analyses have also been performed on such models, and the impact of the slenderness on this structural typology has been studied. Finally, the kinematic theorem of limit analysis has been applied, and some values of collapse acceleration have been consequently computed using different a-priori established collapse mechanisms. The results have been compared with FE simulations results, and the ability of limit analysis to quickly predict the seismic vulnerability has been discussed.