Static Stress Redesign of Structures by Large Admissible Perturbations

2003 ◽  
Vol 127 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Bhineka M. Kristanto
Keyword(s):  
Cross Section ◽  
Forced Response ◽  
Static Stress ◽  
Neutral Axis ◽  
Perturbation Equation ◽  
Cross Sectional ◽  
Structure Changes ◽  
Large Admissible Perturbations ◽  
The Cross ◽  
Outer Fiber

The LargeE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems. The static stress general perturbation equation, which expresses the unknown nodal stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely, the cross-sectional area and moment of inertia, and the distance between the neutral axis and the outer fiber of the cross section. This equation preserves the shape of the cross section in the redesign process. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive finite element (FE) analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Static Stress Redesign of Structures by Large Admissible Perturbations

2003 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Bhineka M. Kristanto
Keyword(s):  
Cross Section ◽  
Forced Response ◽  
Static Stress ◽  
Neutral Axis ◽  
Perturbation Equation ◽  
Cross Sectional ◽  
Structure Changes ◽  
Large Admissible Perturbations ◽  
The Cross ◽  
Outer Fiber

The LargE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems. The static stress general perturbation equation, which expresses the unknown nodal stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends the on the redesign variables for each element or group of elements; namely, the cross-sectional area and moment of inertia, and the distance between the neutral axis and the outer fiber of the cross section. This equation preserves the shape of the cross-section in the redesign process. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FE analyses. Several numerical applications on a simple cantilever beam and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Static Stress Redesign of Plates by Large Admissible Perturbations

2005 ◽  
Author(s):  
Bhineka M. Kristanto ◽  
Michael M. Bernitsas
Keyword(s):  
Plate Thickness ◽  
Forced Response ◽  
Static Stress ◽  
Perturbation Equation ◽  
Shell Elements ◽  
Modal Properties ◽  
General Perturbation ◽  
Structure Changes ◽  
Admissible Perturbation ◽  
Large Admissible Perturbations

The LargE Admissible Perturbation (LEAP) methodology is developed further to solve static stress redesign problems for shell elements. The static stress general perturbation equation, which expresses the unknown stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements; namely the plate thickness. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT which post-processes the FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FEA’s. Several numerical applications on a simple plate and an offshore tower are used to verify the LEAP algorithm for stress redesign.

Static Stress Redesign of Plates by Large Admissible Perturbations

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Bhineka M. Kristanto ◽  
Michael M. Bernitsas
Keyword(s):  
Finite Element Analysis ◽  
Plate Thickness ◽  
Forced Response ◽  
Static Stress ◽  
Perturbation Equation ◽  
Element Analysis ◽  
Shell Elements ◽  
Structure Changes ◽  
The Finite Element Analysis ◽  
Large Admissible Perturbations

The purpose of this paper is to develop further the large admissible perturbation (LEAP) methodology to solve the static stress redesign problem for shell elements. The static stress general perturbation equation, which expresses the unknown stresses of the objective structure in terms of the baseline structure stresses, is derived first. This equation depends on the redesign variables for each element or group of elements, namely, the plate thickness. LEAP enables the designer to redesign a structure to achieve specifications on modal properties, static displacements, forced response amplitudes, and static stresses. LEAP is implemented in code RESTRUCT, which postprocesses the finite element analysis FEA results of the baseline structure. Changes on the order of 100% in the above performance particulars and in redesign variables can be achieved without repetitive FEAs. Several numerical applications on a simple plate and an offshore tower are used to verify the effectiveness of the LEAP algorithm for stress redesign.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Creep Relaxation of a Beam of General Cross Section Subjected to Mechanical and Thermal Loads

1978 ◽  
Vol 100 (4) ◽  
pp. 626-629 ◽  
Author(s):  
M. R. Eslami
Keyword(s):  
Cross Section ◽  
Thermal Load ◽  
Opposite Sign ◽  
Neutral Axis ◽  
Allowable Stress ◽  
Sectional Area ◽  
Lower Stress ◽  
Cross Sectional ◽  
The Cross ◽  
Mechanical Moment

Creep relaxation of a beam of general cross-sectional area subjected to mechanical and thermal load is obtained. Temperature is assumed to be a function of Z, the height of the beam, and the mechanical moment on the cross section M. The stress in the beam is obtained as a function of time. It is concluded that the point of zero stress shifts, and therefore, the neutral axis of the beam moves toward the lower stress magnitude portion of the cross section, and as time passes it sharply drops to a large stress of the opposite sign that for a large enough time will exceed the allowable stress, and therefore causes failure of the beam.

Automated Diagonal Slice and View Solution for 3D Device Structure Analysis

2018 ◽  
Author(s):  
Sang Hoon Lee ◽  
Jeff Blackwood ◽  
Stacey Stone ◽  
Michael Schmidt ◽  
Mark Williamson ◽  
...  
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Image Data ◽  
Planar Surface ◽  
Device Structure ◽  
Cross Sectional ◽  
Device Structures ◽  
The Cross ◽  
Planar Analysis

Abstract The cross-sectional and planar analysis of current generation 3D device structures can be analyzed using a single Focused Ion Beam (FIB) mill. This is achieved using a diagonal milling technique that exposes a multilayer planar surface as well as the cross-section. this provides image data allowing for an efficient method to monitor the fabrication process and find device design errors. This process saves tremendous sample-to-data time, decreasing it from days to hours while still providing precise defect and structure data.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

The Cross Section of Expected Returns with MIDAS Betas

2011 ◽  
Vol 47 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Mariano González ◽  
Juan Nave ◽  
Gonzalo Rubio
Keyword(s):  
Cross Section ◽  
Risk Premium ◽  
Market Risk ◽  
Ordinary Least Squares ◽  
Mixed Data ◽  
Expected Returns ◽  
Data Sampling ◽  
Cross Sectional ◽  
Market Risk Premium ◽  
The Cross

AbstractThis paper explores the cross-sectional variation of expected returns for a large cross section of industry and size/book-to-market portfolios. We employ mixed data sampling (MIDAS) to estimate a portfolio’s conditional beta with the market and with alternative risk factors and innovations to well-known macroeconomic variables. The market risk premium is positive and significant, and the result is robust to alternative asset pricing specifications and model misspecification. However, the traditional 2-pass ordinary least squares (OLS) cross-sectional regressions produce an estimate of the market risk premium that is negative, and significantly different from 0. Using alternative procedures, we compare both beta estimators. We conclude that beta estimates under MIDAS present lower mean absolute forecasting errors and generate better out-of-sample performance of the optimized portfolios relative to OLS betas.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

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