Spine Fin Efficiency – A Three Sided Pyramidal Fin of Isosceles Triangular Cross-Sectional Area

2007 ◽  
Author(s):  
Richard G. Carranza
Keyword(s):  
Closed Form ◽  
Governing Equation ◽  
Heat Balance ◽  
Bessel Functions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Fin Efficiency

An analytical, closed form, solution is presented for determining the fin efficiency of a spine fin with the geometry of a three sided pyramid with isosceles triangular cross-sectional area (from here on referred to as TSPICA). The solution is presented purely in terms of Bessel functions. The TSPICA is modeled using fundamental formulas of geometry. The governing equation is derived from a heat balance around the fin.

Structural Performance of Buried Steel Pipelines Crossing Strike-Slip Faults

2014 ◽  
Author(s):  
Polynikis Vazouras ◽  
Panos Dakoulas ◽  
Spyros A. Karamanos
Keyword(s):  
Closed Form ◽  
Local Buckling ◽  
Closed Form Solution ◽  
Strike Slip ◽  
Form Solution ◽  
Strike Slip Fault ◽  
Performance Criteria ◽  
Cross Sectional ◽  
Soil System ◽  
Inelastic Material

The performance of pipelines subjected to permanent strike-slip fault movement is investigated by combining detailed numerical simulations and closed-form solutions. A closed-form solution for the force-displacement relationship of a buried pipeline subjected to tension is presented and used in the form of nonlinear springs at the two ends of the pipeline in a refined finite element model, allowing an efficient nonlinear analysis of the pipe-soil system at large strike-slip fault movements. The analysis accounts for large deformations, inelastic material behaviour of the pipeline and the surrounding soil, as well as contact and friction conditions on the soil-pipe interface. Appropriate performance criteria of the steel pipeline are adopted and monitored throughout the analysis. It is shown that the end conditions of the pipeline have a significant influence on pipeline performance. For a strike-slip fault normal to the pipeline axis, local buckling occurs at relatively small fault displacements. As the angle between the fault normal and the pipeline axis increases, local buckling can be avoided due to longitudinal stretching, but the pipeline may fail due to excessive axial tensile strains or cross sectional flattening.

Non-Dimensional Finite Element Formulation for Thermal Problems

2012 ◽  
Author(s):  
Sulaman Pashah ◽  
Abul Fazal M. Arif ◽  
Syed M. Zubair
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Finite Element Approach ◽  
Fin Efficiency ◽  
Dimensional Finite Element ◽  
Element Approach

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer; nevertheless the concept of non-dimensional finite element formulation has been applied to a limited type of thermo-fluid problems. The non-dimensional finite element method should provide the dimensionless solution for a given problem. The aim of present work is to develop a non-dimensional thermal finite element for getting dimensionless solution of the problems that do not have a closed form solution. An example is a fin (or extended surface) design. Fin efficiency is a performance characteristic that can be used as design criterion; thus closed form dimensionless solutions for fin efficiency are available in the literature. The results are for different geometry, single material fins. In case, if the fin problem has some geometric and/or material complexities then closed form solutions are not available and finite element approach can be used. However, the obtained finite element solution would not be in dimensionless form. For example, no closed form solutions are available for variable thickness composite fins (i.e. a fin having a base material with a coating over its surface), and the literature shows that finite element solution has been used to study thermal performance of the variable thickness composite fins. Therefore, non-dimensional finite element approach can be applied to directly obtain the dimensionless solution for the problem. The current work consists of presenting a non-dimensional finite element formulation for thermal problems. The element formulation is first validated by solving a test case study that has known closed form solution. The objective is to demonstrate the usefulness of the non-dimensional finite element approach by obtaining dimensionless finite element solutions for some applied problems that do not have a closed form solution.

A closed-form solution for the bending analysis of composite sandwich pipe with compliance core based on high-order sandwich theory

2018 ◽  
Vol 22 (6) ◽  
pp. 1786-1811 ◽  
Author(s):  
I Maleki ◽  
O Rahmani
Keyword(s):  
Closed Form ◽  
Shell Theory ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
High Order ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Nonlinear Distortions ◽  
Flexible Core

In this paper, bending of cylindrical sandwich pipes based on the high-order theory of sandwich structures with flexible core is investigated. The cylindrical sandwich pipe is composed of a flexible core and two composite face sheets. Behavior of the cylindrical sandwich pipe is described by a high-order sandwich shell theory, which explains nonlinear distortions of cross-sectional plane of the flexible core as well as changes in its height. The theory based on variational principles and using an extremely thorough systematic closed-form approach is formulated. In this model, no assumption has been considered for displacement distribution of core components. In this study, stress and displacement of the flexible core are obtained through a three-dimensional elasticity solution and the face sheets are modeled using classical shell theory. Also, a comparison is made in order to verify high-order solution results between a closed-form solution, which is expanded for simply supported boundary conditions and results that are obtained from the commercial finite element method. Finally, influences of physical and geometrical parameters on behavior of the cylindrical sandwich pipe are investigated.

Pelvic Canal Narrowing Caused by Triple Pelvic Osteotomy in the Dog

1994 ◽  
Vol 07 (03) ◽  
pp. 110-113 ◽  
Author(s):  
D. L. Holmberg ◽  
M. B. Hurtig ◽  
H. R. Sukhiani
Keyword(s):  
Postoperative Complications ◽  
Pelvic Osteotomy ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Canal Width ◽  
Operative Complications ◽  
Post Operative Complications

SummaryDuring a triple pelvic osteotomy, rotation of the free acetabular segment causes the pubic remnant on the acetabulum to rotate into the pelvic canal. The resulting narrowing may cause complications by impingement on the organs within the pelvic canal. Triple pelvic osteotomies were performed on ten cadaver pelves with pubic remnants equal to 0, 25, and 50% of the hemi-pubic length and angles of acetabular rotation of 20, 30, and 40 degrees. All combinations of pubic remnant lengths and angles of acetabular rotation caused a significant reduction in pelvic canal-width and cross-sectional area, when compared to the inact pelvis. Zero, 25, and 50% pubic remnants result in 15, 35, and 50% reductions in pelvic canal width respectively. Overrotation of the acetabulum should be avoided and the pubic remnant on the acetabular segment should be minimized to reduce postoperative complications due to pelvic canal narrowing.When performing triple pelvic osteotomies, the length of the pubic remnant on the acetabular segment and the angle of acetabular rotation both significantly narrow the pelvic canal. To reduce post-operative complications, due to narrowing of the pelvic canal, overrotation of the acetabulum should be avoided and the length of the pubic remnant should be minimized.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

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