Finite Element Analysis Solutions Research Articles

Error estimation of nanoindentation mechanical properties near a dissimilar interface via finite element analysis and analytical solution methods

Nanoindentation methods are well suited for probing the mechanical properties of a heterogeneous surface, since the probe size and contact volumes are small and localized. However, the nanoindentation method may introduce errors in the computed mechanical properties when indenting near the interface between two materials having significantly different mechanical properties. Here we examine the case where a soft material is loaded in close proximity to an interface of higher modulus, such as the case when indenting bone near a metallic implant. Results are derived from both an approximate analytical quarter-space solution and a finite element model, and used to estimate the error in indentation-determined elastic modulus as a function of the distance from the apex of contact to the dissimilar interface, for both Berkovich and spherical indenter geometries. Sample data reveal the potential errors in mechanical property determination that can occur when indenting near an interface having higher stiffness, or when characterizing strongly heterogeneous materials. The results suggest that caution should be used when interpreting results in the near-interfacial region.

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

Abstract In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

Pulsed-laser excited thermal lens spectroscopy with sample-fluid heat coupling

Analytical and finite element analysis modeling methods of the pulsed-laser excited photothermal (PT) lens signal of solids samples surrounded by air are presented. The analytical and finite element analysis solutions for the temperatures induced in the sample and in the air were found to agree over the range of conditions in this report. Model results show that the air contribution to the total PT lens signal is significant in many cases. In fact, these solutions open up the possibility of applying the pulsed excited thermal lens method for accurate prediction of the heat transfer to the coupling fluid and subsequently to study the gas surrounding the samples by using a known material solid sample.

Analytical solution for mode-mismatched thermal lens spectroscopy with sample-fluid heat coupling

This paper presents an improved theoretical description of the mode-mismatched thermal lens effect using models that account for heat transport both within the sample and out to the surrounding coupling medium. Analytical and numerical finite element analysis (FEA) solutions are compared and subsequently used to model the thermal lens effect that would be observed using continuous laser excitation. FEA model results were found to be in excellent agreement with the analytical solutions. The model results show that heat transfer to the air coupling medium introduces only a minor effect when compared with the solution obtained without considering axial air-sample heat flux for practical examples. On the other hand, the thermal lens created in the air coupling fluid has a relatively more significant effect on the time-dependent photothermal lens signals.

Modeling the influence of interphase on the elastic properties of carbon nanotube composites

This work investigates the influence of the interphase on the effective properties of carbon nanotube (CNT) composites using finite element analysis and elasticity solutions for representative volume elements. The influence of interphase thickness and gradient in elastic modulus on the elastic properties and stress distribution of the composite is examined, in order to shed some light on experimental parameters that are difficult to measure. It is found that the thickness of the interphase strongly influences the elastic properties and stress distribution of the composite, especially for matrices with low elastic modulus. Modeling results also suggests that the interphase thickness in CNT nanocomposites should be at least of the order of the CNT thickness and that the interphase modulus may follow an exponential gradient.

An Analytical Circuit Model of Switched Reluctance Motors

We have developed a dynamic analytical circuit model to simulate the performance of switched reluctance motors (SRMs). Our model expresses flux linkages as multiple decoupled one-argument functions, either current dependent or rotor position dependent, instead of one two-argument function dependent on both current and rotor position. We propose a novel approach for the computation of the air gap permeance at various rotor positions. By using this analytical model, the performance of a SRM can be simulated very efficiently and with improved accuracy. As an application example, we present a simulation of an 8/6 pole SRM in the system domain, and compare the results with transient finite element analysis (FEA) solutions.

The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses

In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion.

Thermal Stresses Due to Laser Welding in Bridge-Wire Initiators

In ongoing research at the University of Idaho, potential failure mechanisms of airbag initiators are being investigated. Cracking of the cylindrical glass-to-metal seal (GTMS) present in these devices has been observed. These cracks could be a path for moist gas to diffuse into the initiator, potentially leading to bridge-wire degradation and late-fire or no-fire initiator failure. Previous research has shown that cracking may be caused by thermal stresses induced by the GTMS formation process. The goal of this research was to determine if welding of the output-can onto the initiator header could produce stresses in the glass great enough to cause cracking. A finite element analysis solution was chosen to model the transient heat transfer and temperature distribution in the initiator assembly during the welding process. The thermal stresses were calculated with a mechanical analysis once the temperature distribution was determined. Compressive stresses induced by pressing the header assembly into the output-can as part of the manufacturing process were also investigated with a closed-form mechanics of materials solution. The welding thermal stress model initially predicted radial stresses greater than the tangential stresses. This conflicts with observed radial cracks, which would be induced by tangential stresses. Subsequent investigations with an interface region stiffness model showed that when the stiffness of the bond at the pin-glass and glass-header interfaces is decreased, the maximum radial stress is greatly reduced and that the maximum tangential stress stays relatively constant. These predicted stresses were still in excess of the range of glass strengths reported in literature. However, superposition of the compressive stresses due to the press-fit and residual stresses created when the GTMS is formed with these thermal stresses results in the total radial and tangential stresses being on the same order as the reported strengths. It was determined that when initiators are overheated during welding, radial stresses due to thermal expansion cause the bond to fail and separation to occur over a portion of the pin-glass interface. Tangential stresses developed for the same reason are sufficient enough to cause radial cracking, where the bond is still intact.

Development of finite element simulator for forging process design using Euler's fixed meshing method

A simulator based on rigid-plastic finite element method is developed for simulating the plastic flow of material in forging processes. The simulator is specially tailored for the process sign of forging mechanical parts, which is capable to deal with various working conditions and forged materials. In the forging process like backward extrusion, a workpiece normally undergoes large deformation around the tool corners that causes severe distortion of elements in finite element analysis. Since the distorted elements may induce instability of numerical calculation and divergence of non-linear solution in finite element analysis, a computational technique of using the Euler's fixed meshing method is proposed to deal with large deformation problem. This is to replace the conventional way of applying complicated remeshing schemes when using the Lagrange's elements. With this method, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. The proposed method is found to be effective in simulating complicated material flow inside the die cavity, which has many sharp edges, and also the extrusion of relatively slender parts like fins. In this paper, the formulation of rigid-plastic Finite Element Method (FEM) based on plasticity theory for slightly compressible material is introduced, and the advantages of the proposed method as compared to conventional one are discussed.

A new approach to determine the base shear of steel frame structures

Base shear (V) is the maximum lateral force that will occur due to seismic ground motion at the base of a structure. Calculations of base shear depend on a lot of factors such as soil conditions, level of ductility, fundamental period of vibration of the structure, etc. A great number of methodologies have been developed to determine the dynamic responses of individual frameworks. However, there is no well established empirical solution of the dynamic response of the problem due to the base shear of the steel frames. In this study, a formulation based on NN to determine the dynamic response of both braced and unbraced plane steel frames are provided. The presented formulation is a function of number of stories (ns), bays of the frames (nb), and soil types (Z). The training and testing patterns of the proposed NN formulation are obtained from linear Finite Element Analysis (FEA) solution. The NN-based formulation results are compared with the results obtained from numerical and some current design codes. The NN- based formulation results are found to be more accurate.

Finite Element Analysis Using Nonconforming Mesh

A method for finite element analysis using a regular or structured grid is described that eliminates the need for generating conforming mesh for the geometry. The geometry of the domain is represented using implicit equations, which can be generated from traditional solid models. Solution structures are constructed using implicit equations such that the essential boundary conditions are satisfied exactly. This approach is used to solve boundary value problems arising in thermal and structural analysis. Convergence analysis is performed for several numerical examples and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the finite element method in quality but is often less computationally expensive. Furthermore, by eliminating the need for mesh generation, better integration can be achieved between solid modeling and analysis stages of the design process.

Inelastic Shell Instability of Geometrically Imperfect Aluminum Alloy Circular Cylinders under Uniform External Pressure

The paper presents new experimental results on the collapse of unstiffened aluminum alloy circular cylinders suffering elastic and plastic nonsymmetric bifurcation buckling under external hydrostatic pressure. These results complement the results given in two previous Marine Technology papers written by the senior author, which were intended for the structural design of near-perfect unstiffened and ring-stiffened circular conical shells under external hydrostatic pressure. The present paper presents a structural design chart for geometrically imperfect circular cylinders under uniform external pressure, which is more likely to be used than the design charts for the previous near-perfect vessels because it represents the more "usual" case. In addition to an experimental analysis, theoretical analyses were also carried out. An analytical solution by von Mises was used, together with a finite element analysis solution, using the Shell 93 element of the ANSYS computer package. Comparison between ANSYS and the analytical solution was reasonable. A design chart is provided, which looks like it could be quite useful for practical purposes.

Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid

In this study, a method of analysis is presented for investigating the effects of elastic foundation and fluid on the dynamic response characteristics (natural frequencies and associated mode shapes) of rectangular Kirchhoff plates. For the interaction of the Kirchhoff plate–Pasternak foundation, a mixed-type finite element formulation is employed by using the Gâteaux differential. The plate finite element adopted in this study is quadrilateral and isoparametric having four corner nodes, and at each node four degrees of freedom are present (one transverse displacement, two bending moments and one torsional moment). Therefore, a total number of 16 degrees-of-freedom are assigned to each element. A consistent mass formulation is used for the eigenvalue solution in the mixed finite element analysis. The plate structure considered is assumed clamped or simply supported along its edges and resting on a Pasternak foundation. Furthermore, the plate is fully or partially in contact with fresh water on its one side. For the calculation of the fluid–structure interaction effects (generalized fluid–structure interaction forces), a boundary element method is adopted together with the method of images in order to impose an appropriate boundary condition on the fluid's free surface. It is assumed that the fluid is ideal, i.e., inviscid, incompressible, and its motion is irrotational. It is also assumed that the plate–elastic foundation system vibrates in its in vacuo eigenmodes when it is in contact with fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. At the fluid–structure interface, continuity considerations require that the normal velocity of the fluid is equal to that of the structure. The normal velocities on the wetted surface of the structure are expressed in terms of the modal structural displacements, obtained from the finite element analysis. By using the boundary integral equation method the fluid pressure is eliminated from the problem, and the fluid–structure interaction forces are calculated in terms of the generalized hydrodynamic added mass coefficients (due to the inertial effect of fluid). To asses the influences of the elastic foundation and fluid on the dynamic behavior of the plate structure, the natural frequencies and associated mode shapes are presented. Furthermore, the influence of the submerging depth on the dynamic behavior is also investigated.

Finite Element Simulation for Forging Process Using Euler’s Fixed Meshing Method

A simulator based on rigid-plastic finite element method is developed for simulating the plastic flow of material in forging processes. In the forging process likes backward extrusion, a workpiece normally undergoes large deformation around the tool corners that causes severe distortion of elements in finite element analysis. Since the distorted elements may induce instability of numerical calculation and divergence of nonlinear solution in finite element analysis, a computational technique of using the Euler’s fixed meshing method is proposed to deal with large deformation problem by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. With this method, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. The proposed method is found to be effective in simulating complicated material flow inside die cavity which has many sharp edges, and also the extrusion of relatively slender parts like fins. In this paper, the formulation of rigid-plastic finite element method based on plasticity theory for slightly compressible material is introduced, and the advantages of the proposed method as compared to conventional one are discussed.

Seismic response of bridge pier on rigid caisson foundation in soil stratum

An analytical method to study the seismic response of a bridge pier supported on a rigid caisson foundation embedded in a deep soil stratum underlain by a homogeneous half space is developed. The method reproduces the kinematic and inertial responses, using translational and rotational distributed Winkler springs and dashpots to simulate the soil-caisson interaction. Closed-form solutions are given in the frequency domain for vertical harmonic S-wave excitation. Comparison with results from finite element (FE) analysis and other available solutions demonstrates the reliability of the model. Results from parametric studies are given for the kinematic and inertial responses. The modification of the fundamental period and damping ratio of the bridge due to soil-structure interaction is graphically illustrated.

Implicit boundary method for finite element analysis using non‐conforming mesh or grid

AbstractIn the finite element method (FEM), a mesh is used for representing the geometry of the analysis and for representing the test and trial functions by piece‐wise interpolation. Recently, analysis techniques that use structured grids have been developed to avoid the need for a conforming mesh. The boundaries of the analysis domain are represented using implicit equations while a structured grid is used to interpolate functions. Such a method for analysis using structured grids is presented here in which the analysis domain is constructed by Boolean combination of step functions. Implicit equations of the boundary are used in the construction of trial and test functions such that essential boundary conditions are guaranteed to be satisfied. Furthermore, these functions are constructed such that internal elements, through which no boundary passes, have the same stiffness matrix. This approach has been applied to solve linear elastostatic problems and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the FEM in quality but is less computationally expensive for dense mesh/grid and avoids the need for a conforming mesh. Copyright © 2007 John Wiley & Sons, Ltd.

On using a penalty-based cohesive-zone finite element approach, Part I: Elastic solution benchmarks

This paper develops and demonstrates a novel penalty methodology for enhancing the use of the cohesive-zone method (CZM) in finite element models to analyze crack initiation and propagation of surface-bonded structures. For many industrial uses, the CZM finite element approach is troublesome because it is a 3-parameter model depending on critical energy release rate, critical limiting maximum stress and the shape of the traction-separation law. The penalty framework described in the current work maps the CZM approach to fit within the classic Griffith energy release method which is dependent solely on the single material parameter of critical energy release rate. This penalty approach is demonstrated for two generalized problems: double cantilever beam (DCB) analysis and single-arm peeling of very thin elastic substrates. Comparisons with several analytical and pseudo-analytical benchmarks demonstrates how to utilize this new technique as well as the accuracy of the resulting finite element analysis (FEA) solutions for these nonlinear crack propagation and peeling problems.

An inverse method for the determination of full field stresses from experimentally measured normal strains

Certain diffraction-based techniques that measure strains in bulk samples are limited to determination of normal strains. A numerical inverse method is developed to determine full field stresses from the experimentally determined normal strains in isotropic solids under plane stress conditions. The method is based on satisfying the equations of equilibrium and the constitutive relations. The finite difference method is employed to solve the equations and to determine the complete stress field. Furthermore, a least-squares procedure is used to determine the unknown functions of integration in conjunction with known values of shear stress along a reference line. The method is verified by using the normal strain fields in various specimens obtained using both finite element analysis and exact elasticity solutions. It is found that the proposed method predicts the shear stresses accurately in the examples considered.

Ultimate Failure of Debond Damaged Sandwich Panels Loaded with Lateral Pressure — An Experimental and Fracture Mechanics Study

In this study a tool for assessing residual strength of debond damaged laterally loaded sandwich panels is developed. The analysis tool consists of a parametric finite element model and a fracture mechanics calculation procedure to determine the residual strength. The parametric approach allows variation of all geometric and material entities. The fracture mechanics calculation uses crack flank displacements obtained from the finite element analysis solution and experimentally measured mixed-mode fracture toughness values to determine the ultimate failure load. The analysis tool is validated with a number of different ship type panels. Debond criticality is evaluated by using the developed tool and by comparing the test results from panel experiments. The comparison shows that the analysis tool predicts both failure load and failure mode well. The tool can be used to determine the residual strength of different damage cases and has a considerable potential for further development.

Analysis of lateral stability of I-section aluminum beams

This paper focuses on the lateral buckling of laterally-unrestrained aluminum beams subjected to a concentrated, uniformly loading and pure-bending action. The design methods of lateral stability of aluminum beams in the current codes are discussed. The influence of material property on the lateral buckling of aluminum beams is investigated with finite element analysis (FEA) methods. Some numerical examples are given, and the results from current codes are compared with the FEA solutions. The design method on lateral stability of steel beams specified in the Chinese standard GB 50017-2003 is modified to calibrate the stability factors of aluminum beams according to the European code, British code, and American code, and the modified method is verified by FEA results. Through comparison with the available test results, the modified design method for overall stability of aluminum bending members is proposed in this paper and proved applicable in the design of lateral stability of aluminum beams.