Simulation of Cold Bends by Finite Element Method

Residual deformation evaluation of underfill (UF) materials in flip chips is crucial to improve the reliability of electronic packages. In this study, we propose to evaluate the residual thermal strain distributions using an inverse method based on the sampling moiré technique. Even if a grid pattern is fabricated on the specimen at room temperature, the residual strain distributions at an arbitrary temperature relative to the specimen formation temperature can be successfully calculated. The residual strain distributions relative to the free contraction state at an arbitrary temperature can also be measured when the coefficient of thermal expansion is available. A thermal chamber for flip chips was designed under a laser scanning microscope. Using the proposed method, the normal, shear and principal internal strain distributions and deformation characteristics of two kinds of UFs in flip chips were investigated relative to 150 °C. The strains of the UF with low glass transition temperature (UF-A) concentrate near the die material, especially at the die corner, while the strain concentration of the underfill with high glass transition temperature (UF-B) mainly occurs at the die corner and the buffer layer. The maximum principal strain of UF-A is greater than that of UF-B around the die corner. The residual maximum principal strain distributions relative to the free contraction state at 25 °C were compared with the simulation results by the finite element method. The residual strain distribution trends from experiments are consistent with those from simulations.

Skull stiffness of children is of great significance to protect brain tissues during traffic accidents. In this paper, the effects of skull stiffness on traumatic brain injury (TBI) are investigated by using a validated 6-year-old child head finite element (FE) model according to Chinese standard GB/T 24550-2009 Results showed that the HIC value, intracranial pressure, Von Mises stress and shear strain of brain tissue increased with the decrease of skull stiffness during the impact of FE model with engine hood. Therefore, the injury risk of the child head decreases with the increase of skull stiffness. And the skull with higher stiffness can provide a better protection for brain tissues during traffic accidents.

Geometric imperfections play a significant role in the evaluation of the buckling capacity of thin-walled structures. Since the pattern and distribution of such imperfections take a random variation, the determination of a critical imperfect shape that leads to the minimum buckling load becomes a challenge. In this study, an optimization technique based on binary coded genetic algorithms is used together with a nonlinear finite element model to identify the critical imperfection pattern for thin-walled welded structures. The finite element model is based on a consistent sub-parametric shell element that accounts for the effect of both geometric and material nonlinearities. The binary coded genetic algorithm is used as the optimization means to arrive at the imperfection pattern leading to the near globally minimum buckling load. A previously developed mathematical model is employed to describe the imperfection bulges associated with lines of weldment. The method is demonstrated by considering the nonlinear stability analysis of both a circular cylinder subjected to pure axial compressive load and a conical tank under hydrostatic pressure. The combined genetic algorithm – finite element code is used to determine the critical imperfection bulge patterns for the two problems, as well as their associated buckling loads.

The main objective of this work is to check the compatibility of Finite element method (FEM) to determine the modal parameters of the rotor system and to compare the results with analytical method. Current work is an attempt to implement different finite element (FE) models for the estimation of modal parameters. Two different order elements from Beam, Axisymmetric and Solid FE models are considered. The analysis is carried out on the rotor system and the accuracy of the results and the computation time of the FE models are estimated. The FE results are compared with the analytical method. It is observed that FE model can be used to simulate even at higher order frequencies, which is a limitation of analytical model. The analysis shows that the FE results closely match with analytical method and also the study summarizes that proper choosing of FE helps in developing rotor models in both a desirable accuracy and efficiency. Finally, a Campbell diagram is generated using the analytical method and FEM. The critical speeds are also calculated from the Campbell diagram. The closeness of the results between the two methods is checked.

Purpose – In former work, test results of cracks in aluminium panels under cyclic shear buckling showed that cracks in the tensile stress field of a buckle propagate. The main influencing factor for the crack growth rate is the maximum principle stress. A simplified approach for crack propagation analyses based on this finding showed limitations for application on larger cracks because it disregarded the increasing out-of-plane deformation for larger cracks as well as stress redistributions. The purpose of this paper is to improve the results of the simplified approach with the help of finite element method (FEM). Design/methodology/approach – An approach for crack propagation based on FEM is presented taking into account the mutual interaction of cracks and buckling. The finite element (FE) model, which is described in detail, respects the boundary conditions of the test-set-up. Different initial crack positions, loads and panel thicknesses are analyzed. Results of the stress intensity factors KI calculated by the ABAQUS® FE model provide a function which is used to run a crack propagation analysis based on Forman law. Findings – The results of the FE-based crack propagation solution are in good agreement with test results and improve the prediction of the simplified approach. It is not restricted in terms of panel thickness, crack position or applied shear load. Research limitations/implications – Limitations of the FE-based crack propagation solution compared to the experimental results are discussed. These are, the sensitivity of crack propagation analyses to initial crack length and deviations of the experimental settings from the ideal FE model. Originality/value – The interaction of cracks and buckling in aluminium shells is mainly disregarded both in research and industrial work, but can be of interest considering, accidental damages in fuselage side shells. Cracks propagate under shear load as it was shown in former work. The FE modeling of the tests presented in this paper proves the mutual interactions of crack propagation and buckling deformation.

Heat curving is a practical and economical process used by steel fabricators for curving structural steel. In this method, the flange edges of a fabricated straight girder are asymmetrically heated to induce residual curvature on cooling. Available analytical methods for predicting the resulting residual stress, strain and curvature are complex and iterative because of the need to account for material and geometric non-linearity. This paper presents a single-step, non-iterative, numerical procedure for determining the effects of heat-curving on residual stress and strain based on a previously developed simplified analysis. Thermal equilibrium equations for idealized heating profiles are first recast in a general parametric form and then solved numerically for standard heating width and temperature using modern technical computing. The resulting solutions are expressed as polynomial functions to allow the solution space for the residual curvature to be graphically represented. Curvature predictions using this simplified approach are shown to be within 11% of measured values and within 5% of values obtained using more rigorous numerical methods.Highlights The paper presents a simplified computational method for heat curving steel. Equations for non-linear stress distribution are cast in a parametric form and solved numerically using Wolfram Mathematica V.9.0 computer algebra package. Solutions are presented as polynomials and graphical plots to directly calculate the curvature. Legitimacy is confirmed based on comparisons with available experimental and theoretical values.

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.

This paper is concerned with the orthotropic problem of diaphragm-type air springs which consist of rubber linings, nylon reinforced rubber composite and bead ring. The analysis is carried out with a finite element method developed to consider the orthotropic properties, geometric nonlinearity using four-node degenerated shell element with reduced integration. Physical stabilization scheme is used to control the zeroenergy mode of the element. The analysis includes an inflation analysis and a lateral analysis of an air spring for the deformed shape and the spring load with respect to the vertical and l ateral deflection. Numerical results demonstrate the variation of the outer diameter, the fold height, the vertical force and the lateral force with respect to the inflation pressure and the lateral deflection.

Collapse of transmission towers due to downbursts is often initiated by local failure of key structural members, while the local failure of key structural members is related to local material and geometrical nonlinearities. This paper presents a multi-scale finite element (FE) model for the failure analysis of transmission towers under downburst-induced wind loading. The potential local failure areas of the tower are modeled by shell or solid elements, and the remaining parts by beam elements. In this way, the failure of the tower can be accurately simulated on the one hand and the computational effort can be reduced on the other hand. This paper first introduces how to determine the downburst-induced wind loading on transmission towers. Both the conventional beam and multi-scale FE models of the transmission tower are then developed and used in the failure analysis. A comparison of the failure results obtained by the two FE models show that the multi-scale FE model can effectively simulate the stress concentration of angle members around the bolt connections and the cross-section plastic collapse of key structural members, leading to a different failure pattern for the tower from the conventional FE method. It is suggested that the multi-scale FE model should be used for better accuracy in the failure analysis of transmission towers under downburst loading.

The purpose of this paper is to study two types of knee prosthesis that are based on the Finite Element Method (FEM). The process to generate the Finite Element (FE) models was conducted in several steps. A 3D geometric model of a healthy knee joint was created using 3D scanned data from an anatomical knee model. This healthy model comprises a portion of the long bones (femur, tibia and fibula) as well as by the lateral and medial meniscus, cartilage and ligaments. The digital model that was obtained was repaired and converted to an engineering drawing format using CATIA© software. Based on the foregoing format, two types of artificial knee prostheses were designed and assembled. Mentat Marc© software was used to model the healthy and artificial knee FE models. The healthy and artificial knee FE models were subjected to different loads. The an-thropometry of the human body that was studied and the combination of loads to apply to the knee were obtained by use of 3D Static Strength Prediction software (3DSSPP©). The Von Mises stresses, as well as all the relative displacements of the components of the healthy and artificial knee FE model, were obtained from the Mentat Marc© software. The Von Mises stresses for both the cortical and the trabecular bone of the artificial and healthy knee FE model were analyzed and compared. The stresses that were obtained from the two knee prosthesis that were studied based on the artificial FE models were very similar to those stresses that were obtained from healthy FE models.

The paper reviews a development of mathematical algorithms and implementation of mapping residual stress profiles from microscale to macroscale finite element (FE) models. A shot-peening simulation of Inconel 718 is conducted using the finite element method (FEM) to obtain the residual stress profiles which are used as an input in the developed mapping algorithms. Residual stress profiles induced by the shot-peening processes are mapped into different FE models including a perforated plate, a model with a complex surface, and an aero-engine vane component. The mathematical mapping algorithms and formulations are developed for 2D and 3D FE models where residual stress profiles obtained experimentally, numerically, or analytically for different manufacturing processes including shot-peening, water jet machining, milling, turning, roller burnishing, laser machining and peening, electro discharge machining, etc., can be mapped on FE models with complex geometries. The implementation and the results for the mapping techniques are presented and discussed in detail.

The object of research is cured thermosetting epoxy polymer and FRP on the base of the same polymer matrix. The purpose of this research is to develop the finite element (FE) method in the modeling of cured thermosetting polymers and FRPs to predict their mechanical and thermal properties. The structural mathematical modeling with subsequent computer FE modeling was performed. The results of FE modeling were compared with the experimental data of cured polymer's and FRP's tensile strength and deformations under mechanical load at different temperatures. The design of the polymer's FE model was based on the tetrahedral supramolecular structure and then transformed into FRP's model by integrating glass fiber rods. Using the structural density as the structure model's parameter, the relative size and disposition of the finite elements were determined. The viscoelastic properties are set in the model by regulating the structural density and compressive/tensile properties of joints. The long-term plastic deformation and stress relaxation were determined as the result of the supramolecular structure's inner shearing with the decrease of its structural density. The FE models of the cured epoxy polymer and FRP were developed, making it possible to predict short-term and long-term deformations under load with high accuracy considering the temperature factor.

The cold bended parts of pipelines are prone to geotechnical movements due to discontinuous permafrost, slope instabilities and seismic activities. Sen et al carried out an extensive experimental study in 2006 in order to understand the buckling behaviour of cold bend pipes under applied curvature. In one of the experiments in this study, a high pressure X65 pipe specimen failed under applied curvature due to tension side fracture. This fracture was observed after the development of a wrinkle on the compression side. In this paper, the behaviour of this cold bend pipe specimen under applied curvature and bending is investigated using finite element method to understand the conditions leading to pipe body tension side fracture in the post-buckling phase of a cold bend. The finite element analyses - with and without internal pressure and the plastic strain and von Mises stress distributions - showed that the tension side fracture occurs under equal amount of applied curvature only in the case of the pressurized pipes. These results were in accordance with the experimental results obtained by Sen et al. The effect of internal pressure is analyzed further in order to determine a transition point of the mode of failure from compressive to tensile. A parametric study is conducted for a series of internal pressure values ranging from 20% Specified Minimum Yield Strength (SMYS) to 80% SMYS. A failure criterion based on the equivalent plastic strain reaching a critical value was used to assess the models behavior up to failure. It was observed that load cases having an internal pressure less than or equal to 60% SMYS exhibit higher equivalent plastic strains on the compression side throughout the simulations and up to failure. However, for internal pressure values higher than or equal to 67% SMYS, the equivalent plastic strain on the tension side of the cold bend starts increasing dramatically at some point during the loading process, exceeding the equivalent plastic strain values on the compression side up to failure.

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling