A Pipe Bend Subject to a Uniformly Distributed Radial Force

2012 ◽  
Author(s):  
Joseph M. Mazzeo
Keyword(s):  
Radial Force ◽  
Piping System ◽  
Curved Beam ◽  
Pipe Bend ◽  
Beam Elements ◽  
Straight Beam ◽  
Uniform Cross Section ◽  
Single Force ◽  
Direct Stiffness ◽  
Small Deformations

The effects of a distributed radial load on an elbow or bend within a piping system, caused by large changes in momentum due to fluid flow, are often represented by a single force. The method presented here will result in more accurate results. In this paper, equations are derived to predict deformations of a pipe bend or curved beam cantilever at its free end due to a uniformly distributed radial force. Assuming isotropic, linearly elastic materials of uniform cross section, uniform bend radius, and small deformations, equations are derived using Castigliano’s theorem. Deformation due to shear and axial stresses is also considered. Derived equations are validated through a case example which compares them to a model consisting of a number of straight beam elements assembled to model a curved beam. The example demonstrates that free end deformations can be integrated into a piping analysis program by using the direct stiffness method in order to obtain the resulting displacements, forces, and moments that result from restraint of the bend due to the stiffness of the attached pipe.

An Investigation Into the Effects of Curved Beam Elements on the Out-of-Plane Stiffness Profile in a Compliant Large-Displacement Finger

2013 ◽  
Author(s):  
Valerie Y. Goemans ◽  
Just L. Herder ◽  
Mary I. Frecker
Keyword(s):  
Range Of Motion ◽  
Compliant Mechanisms ◽  
Large Displacement ◽  
Curved Beam ◽  
Trade Off ◽  
Beam Elements ◽  
Straight Beam ◽  
Double Beam ◽  
Out Of Plane ◽  
Stiffness Profile

Compliant mechanisms have many advantages over rigid-link mechanisms. However, one of the challenges of compliant mechanisms is the trade-off between a large range of motion and a high out-of-plane stiffness. Furthermore, the out-of-plane stiffness is shown to vary over the range of motion. Especially for large-displacement compliant mechanisms this can be by a significant amount. In this paper the use of curved beam elements in a compliant mechanism is shown to have impact on this trade-off. The influence of curved beam elements on the out-of-plane stiffness over the entire range of motion is presented for simple structures such as a single beam element and double beam elements, as well as a compliant finger. With the use of a genetic algorithm optimization, the difference in performance of a design with only straight beam elements versus one with curved beam elements is highlighted and the effect on the out-of-plane stiffness profile is presented. The optimization with curved beam elements results in solutions with a performance in terms of objective function values that cannot be found by the optimization with only straight beam elements. It is shown that for simple structures the use of curved beam elements has a large influence on the shape of the out-of-plane stiffness profile along the range of motion, while for the compliant finger the influence is mainly in the variables of the out-of-plane stiffness profile.

A Pipe Bend Subject to a Uniformly Distributed Radial Force

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Joseph M. Mazzeo
Keyword(s):  
Fluid Flow ◽  
Radial Force ◽  
Piping System ◽  
Potential Importance ◽  
Radial Load ◽  
Pipe Bend ◽  
Modeling Methods ◽  
Momentum Change ◽  
Simplified Modeling ◽  
Change Forces

The effects of a distributed radial load on an elbow or bend within a piping system, caused by changes in momentum due to fluid flow, can be represented by one or more point loads. Simplified methods result in inaccurate results in some cases. Modeling the bend with multiple nodes and forces increases accuracy. The method presented here will provide accurate results, comparable to breaking up the bend into many nodes and forces. A number of example analyses are presented for comparison with simplified modeling methods and the potential importance of considering momentum change forces in some power piping geometries are discussed.

Effect of Bend Angle on Gross Plastic Deformation of Pipe Bends: A Finite Element Based Study

2015 ◽  
Author(s):  
Anindya Bhattacharya ◽  
Sachin Bapat ◽  
Hardik Patel ◽  
Shailan Patel
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Failure Mechanisms ◽  
Bending Moment ◽  
Bend Angle ◽  
Piping System ◽  
Plastic Collapse ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bend Angles

Bends are an integral part of a piping system. Because of the ability to ovalize and warp they offer more flexibility when compared to straight pipes. Piping Code ASME B31.3 [1] provides flexibility factors and stress intensification factors for the pipe bends. Like any other piping component, one of the failure mechanisms of a pipe bend is gross plastic deformation. In this paper, plastic collapse load of pipe bends have been analyzed for various bend parameters (bend parameter = tRbrm2) under internal pressure and in-plane bending moment for various bend angles using both small and large deformation theories. FE code ABAQUS version 6.9EF-1 has been used for the analyses.

Energy Harvesting From Arterial Blood Pressure for Embedded Brain Sensing

2016 ◽  
Author(s):  
Aditya Nanda ◽  
M. Amin Karami
Keyword(s):  
Blood Pressure ◽  
Transfer Function ◽  
Arterial Blood Pressure ◽  
Radial Pressure ◽  
Radial Breathing Mode ◽  
Curved Beam ◽  
Induced Voltage ◽  
Governing Equations ◽  
Arterial Blood ◽  
Straight Beam

This paper investigates energy harvesting from arterial blood pressure via the piezoelectric effect for the purpose of powering embedded micro-sensors in the brain. Blood flow is highly dynamic and arterial blood pressure varies, in the average human blood vessel, from 120 mm of Hg to 80 mm of Hg and we look at transduction of this pressure variation to electric energy via the piezoelectric effect. We propose two different geometries for this purpose. Initially, we look at the energy harvested by a cylinder, coated with PVDF (Polyvinylidene fluoride) patches, placed inside an artery acted upon by blood pressure. The arrangement is similar to that of a stent which is a cylinder placed in veins and arteries to prevent obstruction in blood flow. The governing equations of the harvester are obtained using Hamilton’s principle. Pressure acting in arteries is radially directed and this is used to simplify the governing equations. Specifically, radial pressure directed on the inner wall of the cylinder is assumed to excite only the radial breathing mode of vibration. Using this, the transfer function relating pressure to the induced voltage across the surface of the harvester is derived and the power harvested by the cylindrical harvester is obtained for different shunt resistances. However, the natural frequency of the radial breathing mode (RBM) is found to be very high and the harvested power at the frequencies of interest (3 Hz – 20 Hz) is very low. To decrease the natural frequency, we propose a novel streaked cylinder design that involves cutting the cylinder along the length, transforming it to a curved beam with an opening angle of 360 deg.. The governing equations corresponding to a circular curved beam, with PVDF patches on top and bottom surfaces, are derived using Hamilton’s principle and modal analysis is used to obtain the transfer function relating radial pressure to induced voltage. We validate the derived transfer function by evaluating the harvested power for a beam with very large radius of curvature; in which case, the curved beam becomes a straight beam and the harvested power is compared with the same for a straight beam (which exists in the literature). Further, we conduct design analyses and obtain the power as the geometric parameters of the harvester are varied for the purpose of optimizing the dimensions of harvester for maximal power generation. The power harvested by the harvester, at lower frequencies is deemed to be satisfactory.

Inelastic Response of Nuclear Piping Subjected to Rupture Forces

1976 ◽  
Vol 98 (2) ◽  
pp. 98-104 ◽  
Author(s):  
J. C. Anderson ◽  
A. K. Singh
Keyword(s):  
Dynamic Response ◽  
Numerical Procedure ◽  
Beam Element ◽  
Piping System ◽  
Curved Beam ◽  
Blow Down ◽  
Curved Beam Element ◽  
Piping Systems ◽  
Support Element ◽  
System 1

A numerical procedure which can be used to evaluate the inelastic dynamic response of piping systems subjected to blow-down forces is described. The following finite elements are used to represent the piping system: (1) bilinear beam element, (2) bilinear curved beam element, and (3) bilinear support element with an initial gap. The method is then used to evaluate the dynamic response of two typical segments of a main steamline.

Piping System Structural Integrity Simulation for Post LOCA Water Hammer Loads

2002 ◽  
Author(s):  
B. W. Manning ◽  
T. Stevens ◽  
G. Morandin ◽  
R. G. Sauve´ ◽  
R. Richards ◽  
...  
Keyword(s):  
Structural Damage ◽  
Structural Integrity ◽  
Water Hammer ◽  
Piping System ◽  
Linear Modeling ◽  
Linear Elastic ◽  
Beam Elements ◽  
Loss Of Coolant Accident ◽  
Loss Of Coolant ◽  
Non Linear

The Canadian Nuclear Safety Commission (CNSC) required as part of the operating license for Ontario Power Generation’s Darlington Nuclear Generating Station, that the structural integrity of the piping following a loss of coolant accident (LOCA) be demonstrated. This is necessary to ensure that no subsequent pressure boundary failures will impede the ability to maintain fuel cooling. The injection of cold emergency coolant following a LOCA creates the potential for the occurrence of condensation-induced water hammers (CIWH) in the primary heat transport (PHT) system piping. Classical linear elastic piping analysis using the class 1 NB-3656 rules of the ASME Boiler & Pressure Vessel Code failed to demonstrate the adequacy of the piping and/or its supports that were designed using the linear elastic rules of subsection NF for nine of the twelve piping models that comprise the PHT system. A decision was made to undertake a state-of-the-art non-linear explicit analysis in order to qualify the piping. Strain rather than stress limits would be applied similar to those being developed by ASME for nuclear packaging undergoing accidental impact during transportation. In order to address the feasibility of this approach, a non-linear analysis was performed on a portion of one of the piping systems. The piping was modeled as shells and again as beam elements with and without detailed modeling of the supports. After these initial simulations, it was determined that the piping could be modeled with simplified beam elements, however, the supports would require a more detailed modeling in order to determine the extent of support damage and the effect the supports have on the integrity of the piping system itself. This paper addresses the non-linear modeling of the piping models and discusses the modeling details, assumptions and analysis results. This approach is shown to be a useful alternative for predicting the extent of structural damage that can be expected by a Level D event such as a condensation induced water hammer following a loss of coolant accident.

Natural frequencies of a rotating curved cantilever beam: A perturbation method-based approach

2020 ◽  
Vol 234 (9) ◽  
pp. 1706-1719
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Perturbation Method ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Analytical Formula ◽  
Industrial Applications ◽  
Curved Beam ◽  
Straight Beam ◽  
Element Method

The blades of propellers, fans, compressor and turbines can be modeled as curved beams. In general, for industrial application, finite element method is employed to determine the modal characteristics of these structures. In the present work, a novel formula for determining the natural frequencies of a rotating circularly curved cantilever beam is derived. Rayleigh–Ritz approach is used along with perturbation method to obtain the analytical formula. In the first part of the work, a formula for natural frequencies of a non-rotating curved beam vibrating in its plane of curvature is presented. This formula is derived as a correction to the natural frequencies of its straight counterpart. The curvature is treated as a perturbation parameter. In the next part of the work, the effect of rotation on the curved beam is captured as an additional perturbation. Thus, the formula for a curved rotating beam is derived as a correction (involving two perturbation parameters) to the non-rotating straight beam. The results obtained using the derived formula are compared with the finite element method results. It is found that the frequency estimates from the formula are valid over a fairly large range of curvature and rotation speed. Thus, the derived formula can provide a faster alternative for design iterations in industrial applications.

A Finite Element Modeling Framework for Planar Curved Beam Dynamics Considering Nonlinearities and Contacts

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Tianheng Feng ◽  
Soovadeep Bakshi ◽  
Qifan Gu ◽  
Dongmei Chen
Keyword(s):  
Finite Element ◽  
Beam Dynamics ◽  
Curved Beam ◽  
Shape Functions ◽  
Curved Beams ◽  
Modeling Framework ◽  
External Wall ◽  
Beam Elements ◽  
High Compression ◽  
Assumed Strain

Motivated by modeling directional drilling dynamics where planar curved beams undergo small displacements, withstand high compression forces, and are in contact with an external wall, this paper presents an finite element method (FEM) modeling framework to describe planar curved beam dynamics under loading. The shape functions of the planar curved beam are obtained using the assumed strain field method. Based on the shape functions, the stiffness and mass matrices of a planar curved beam element are derived using the Euler–Lagrange equations, and the nonlinearities of the beam strain are modeled through a geometric stiffness matrix. The contact effects between curved beams and the external wall are also modeled, and corresponding numerical methods are discussed. Simulations are carried out using the developed element to analyze the dynamics and statics of planar curved structures under small displacements. The numerical simulation converges to the analytical solution as the number of elements increases. Modeling using curved beam elements achieves higher accuracy in both static and dynamic analyses compared to the approximation made by using straight beam elements. To show the utility of the developed FEM framework, the post-buckling condition of a directional drill string is analyzed. The drill pipe undergoes spiral buckling under high compression forces, which agrees with experiments and field observations.

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