Pure Bending of Curved Beams of Thin-Walled Rectangular Box Section

1991 ◽  
Vol 58 (1) ◽  
pp. 154-156 ◽  
Author(s):  
R. D. Cook
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Circumferential Stress ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Element Analyses ◽  
Curved Beams ◽  
Pure Bending ◽  
The Subject ◽  
Thin Walled

A closed-form solution of the subject problem is presented. The analytical method resembles that used by Bleich (1933) to study curved beams of I or T section. It is found that the circumferential stress may be smaller than a perpendicular stress that arises from flexing of parts of the box. Accuracy of the solution is verified by comparison with finite element analyses.

A New Analytical Method for Calculating Maximum Junction Temperature of Packaged Devices Incorporating the Temperature Distribution at the Base of the Substrate

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Finite Element ◽  
Temperature Distribution ◽  
Analytical Method ◽  
Analytical Methods ◽  
Thermal Analyses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Uniform Temperature ◽  
Element Analysis

All current analytical methods for calculating junction temperature of field effect transistor (FET) and monolithic microwave integrated circuits (MMIC) devices have assumed a constant uniform temperature at the base of the substrate. In a packaged device, however, where the substrate is attached to a carrier, finite element thermal analyses have shown that the temperature distribution along the base of the substrate is not uniform but has a bell-shaped distribution. Consequently, current analytical methods which attempt to predict the junction temperature of a packaged MMIC device by assuming a constant uniform temperature at the base of the substrate have been found to be inaccurate. In this paper, it is found that the temperature distribution along the base of a substrate can be well approximated by a Lorentz distribution which can be determined from a few basic parameters of the device such as the gate length, gate pitch, number of gates, and length of substrate. By incorporating this Lorentz temperature distribution at the base of the substrate with a new closed-form solution for the three-dimensional temperature distribution within the substrate, a new analytical method is developed for accurately calculating the junction temperature of MMIC devices. The accuracy of this new method has been verified with junction temperatures of MMIC devices measured using thermoreflectance thermography (TRT) as well as those calculated using finite element analysis (FEA).

Master curves for Hertzian indentation on coating/substrate systems

2004 ◽  
Vol 19 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Chun-Hway Hsueh ◽  
Pedro Miranda
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Coating Thickness ◽  
Closed Form Solution ◽  
Form Solution ◽  
Contact Radius ◽  
Finite Element Analyses ◽  
Master Curves ◽  
Modulus Ratio ◽  
Hertzian Indentation

An analytical model was developed to derive an approximate closed-form solution for indenter displacement when a rigid spherical indenter is pressed onto a coating/substrate system. Finite element analyses were also performed to verify the analytical solution. The results showed that the solution could be obtained from the analytical expression for Hertzian indentation on a homogeneous semi-infinite elastic medium multiplied by a modification term. This modification term is a function of two ratios: (i) Young’s modulus ratio between the coating and the substrate and (ii) the ratio between the coating thickness and the contact radius. Based on this modification term, master curves for Hertzian indentation on coating/substrate systems were plotted.

Semi-Closed-Form Displacement Equations for Calculating J-R Curves From Pipe Fracture Experiments

2015 ◽  
Author(s):  
Richard Olson ◽  
Ben Thornton
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strain Curve ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
Form Solution ◽  
Finite Element Analyses ◽  
Pipe Bend ◽  
Point Bend

The equations to generate a J-R curve from a four-point bend test on circumferentially cracked pipe have been known for many years. Given the experimental pipe load-displacement record and crack growth, the only impediment to routinely calculating pipe J-R curves is the requirement to know the non-cracked pipe elastic and plastic displacements. Traditionally, finite element analyses are used to find these displacements. This paper presents a semi-closed-form solution for the total (elastic plus plastic) non-cracked pipe displacements that eliminates the need to perform finite element analyses to calculate a pipe J-R curve. Using a Ramberg-Osgood nonlinear representation of the stress-strain curve and the assumption that plane sections remain plane, beam bending equations can be written to find nonlinear beam displacements for pipe bend geometries with a base metal crack. Building on this result, the solution is extended to the dissimilar metal weld (DMW) case with five nonlinear materials. The non-cracked pipe displacement solutions are presented as well as comparisons using these equations between compact tension specimen J-R toughness curves and J-R curves from pipe experiments.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

Design and finite element assessment of fully uncoupled multi-directional layups for delamination tests

2019 ◽  
Vol 54 (6) ◽  
pp. 773-790 ◽  
Author(s):  
Torquato Garulli ◽  
Anita Catapano ◽  
Daniele Fanteria ◽  
Julien Jumel ◽  
Eric Martin
Keyword(s):  
Finite Element ◽  
Crack Closure ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Standard Test ◽  
Form Solution ◽  
Virtual Crack Closure Technique ◽  
Test Procedures ◽  
Closure Technique ◽  
Double Cantilever Beam Test

In this paper, a procedure to obtain fully uncoupled multi-directional stacking sequences for delamination specimens is outlined. For such sequences, in-plane, membrane-bending and torsion–bending coupling terms are null (in closed-form solution in the framework of classical laminated plate theory) for the entire stack and for both its halves, which form two arms in the pre-cracked region of a typical delamination specimen. This is achieved exploiting the superposition of quasi-trivial quasi-homogeneous stacking sequences, according to appropriate rules. Any pair of orientations of the plies embedding the delamination plane can be obtained. To assess the effectiveness of the proposed approach, a fully uncoupled multi-directional sequence is designed and compared to other relevant sequences proposed in the literature. Finite element simulations of double cantilever beam test are performed using classic virtual crack closure technique and a revised state-of-the-art virtual crack closure technique formulation too. Some interesting conclusions regarding proper design of multidirectional stacks for delamination tests are drawn. Moreover, the results confirm the suitability of fully uncoupled multi-directional sequences for delamination tests. Thanks to their properties, these sequences might lay the foundations for the development of standard test procedures for delamination in angle-ply interfaces.

scholarly journals Linearizing Control of a Distributed Actuation Magnetic Bearing for Thin-Walled Rotor Systems

Actuators ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 99
Author(s):  
Chakkapong Chamroon ◽  
Matthew O.T. Cole ◽  
Wichaphon Fakkaew
Keyword(s):  
Closed Form Solution ◽  
Magnetic Bearing ◽  
Form Solution ◽  
Electromagnetic Actuators ◽  
Control Approach ◽  
Zero Current ◽  
Improved Stability ◽  
Gradient Based ◽  
Thin Walled ◽  
Coil Winding

This paper describes an exact linearizing control approach for a distributed actuation magnetic bearing (DAMB) supporting a thin-walled rotor. The radial DAMB design incorporates a circular array of compact electromagnetic actuators with multi-coil winding scheme optimized for supporting thin-walled rotors. A distinguishing feature is that both the x and y components of the radial bearing force are coupled with all four of the supplied coil currents and so a closed form solution for the linearizing equations cannot be obtained. To overcome this issue, a gradient-based root-finding algorithm is proposed to solve the linearizing equations numerically in real-time. The proposed method can be applied with any chosen constraints on current values to achieve low RMS values while avoiding zero-current operating points. The approach is implemented and tested experimentally on a rotor system comprising two radial DAMBs and a uniform cylindrical shell rotor. The results show that the method achieves more accurate reproduction of demanded bearing forces, thereby simplifying the rotor suspension control design and providing improved stability and vibration control performance compared with implementations based on operating point linearization.

Identification of cracks in an Euler–Bernoulli beam using Bayesian inference and closed-form solution of vibration modes

2020 ◽  
pp. 146442072096971
Author(s):  
Tianyu Wang ◽  
Mohammad Noori ◽  
Wael A. Altabey
Keyword(s):  
Finite Element ◽  
Bayesian Inference ◽  
Finite Element Model ◽  
Crack Detection ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Vibration Modes ◽  
Vibration Data ◽  
The Finite Element Model

Over the past two decades, extensive research has been carried out in the field of structural health monitoring for damage detection in structural systems. Some crack detection methods are based on the finite element model of a beam and use vibration data are developed. These methods identify the crack by updating of the finite element model according to the vibration data of structure. This paper proposes a novel method for crack detection in Euler–Bernoulli beams based on the closed-form solution of mode shapes using Bayesian inference. The expression of vibration modes is derived analytically with the crack parameters as unknown variables. Subsequently, the Bayesian inference is used to obtain the probability density function of crack parameters and to evaluate the uncertainty of the modes. Finally, the method is applied to a series of numerical examples, including a beam with a single-crack and multi-cracks, to verify the effectiveness of this method.

scholarly journals Performance of New Austrian Tunneling Method (NATM) in Weak Rock Case Study

2018 ◽  
Vol 7 (4.20) ◽  
pp. 40
Author(s):  
Heba Kamal ◽  
. .
Keyword(s):  
Finite Element ◽  
Closed Form Solution ◽  
Side Wall ◽  
Form Solution ◽  
Two Dimensional ◽  
Phase 2 ◽  
Actual Case ◽  
Tunneling Method ◽  
New Austrian Tunneling Method

The decline in the over ground utilizable space and increment in development of metro structures, cut and cover structures are winding up fairly difficult to conceptualize and build. In this examination, a nonlinear two dimensional limited component investigation was completed to show the New Austrian Tunneling Method (NATM) burrow developed in frail shake utilizing the business limited component with joint programming PHASE 2.The validity of the numerical modeling procedure performed by the author was checked by making back-analysis for an actual case study of Strengen Tunnel which is one of the biggest expressways in western Austria.  A comprehensive parametric study was performed on a hypothetical circle tunnel. Two dimensional numerical simulations with the finite element with joint software PHASE 2 have been performed to ground behaviour with   the results of the numerical analysis are presented and   discussed for recommendations for future work. In general the tangential stress at side wall and crown  obtained from  finite element with joints are  nearly equal or higher than the closed form solution and equivalent continuum.                                                                                   

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