Generation and Use of Simplified Uplift Shape Functions in Unanchored Cylindrical Tanks

1996 ◽  
Vol 118 (3) ◽  
pp. 278-286 ◽  
Author(s):  
D. T. Lau ◽  
X. Zeng
Keyword(s):  
Mathematical Model ◽  
Bottom Plate ◽  
Shape Functions ◽  
Liquid Storage ◽  
Tilt Condition ◽  
Liquid Storage Tank ◽  
Cylindrical Tanks ◽  
Relationship Of ◽  
The Relationship ◽  
Simplified Mathematical Model

This paper presents a simplified mathematical model for modeling the flexible bottom plate in an unanchored cylindrical liquid storage tank partially uplifted under the static tilt condition. In this model, the cylindrical tank is divided into substructures according to the deformation-resistant mechanisms involved. The modeling of each substructure is based on the Ritz formulation. Numerical results are presented and compared with reported experimental measurements. The results show that the simplified mathematical model is efficient. Practical and accurate results can be obtained using the model leading to a better understanding of the uplift mechanism. The relationship of the uplift behavior with the static tilt angle is also presented and discussed.

scholarly journals Relation between swine weight and morphometric measurements

2020 ◽  
Vol 9 (9) ◽  
pp. e891998013
Author(s):  
Mônica Calixto Ribeiro de Holanda ◽  
Marco Aurélio Carneiro de Holanda ◽  
Leandro Ricardo Rodrigues de Lucena
Keyword(s):  
Mathematical Model ◽  
Body Weight ◽  
Regression Models ◽  
Hip Circumference ◽  
Morphometric Measurements ◽  
Large White ◽  
Male And Female ◽  
Lactation Phase ◽  
Relationship Of ◽  
The Relationship

Objective was to define a mathematical model that better explain the relationship of the animals weight depending not only on the animals age but also on the animals morphometric measurements. 40 piglets, half Duroc-Large White blood, were used, 20 males and 20 females, from 3 to 35 days of age (lactation phase) initially weighing 1.518 ± 0.121 kg and from 36 to 66 days of age (calving phase) with a body weight of 7.010 ± 0.704 kg. The animals were weighed weekly on a digital balance. The relationship of animal weight, age and morphometric measurements of male and female piglets were performed using regression models: existing, linear and power. The models were evaluated according to nine criterialinear model was the most adequate to explain the weight of male pigs, while for female pigs was the power. The age of the pig, the shank and palette length, as well as the circumference of the shank jointly explain the weight of the male piglets. The weight of females is explained jointly by age, body length, thorax and hip circumference.

Establishment of Relatively Unified Mathematical Model for Spiral Surface Based on Movement Characteristics of Particle

2010 ◽  
Vol 455 ◽  
pp. 1-5
Author(s):  
L.Z. Song ◽  
S.L. Guo ◽  
Chun Jiang Xiang ◽  
Qi Hong
Keyword(s):  
Mathematical Model ◽  
Surface Shape ◽  
Movement Characteristics ◽  
Spiral Surface ◽  
Relationship Of ◽  
First Time ◽  
The Relationship

From the viewpoint of the forming principle of spiral curve and classification from the kinematics, established relatively unified mathematical model of spiral curve based on the movement characteristics of particle and the forming principle of space surface shape, and in turn relying on relatively unified mathematical model of spiral curve, combined the similarity of forming movement between spiral curve and spiral surface, derived the relatively unified mathematical model of spiral surface with the concept of sequence of operator presented for the first time. The relatively unified mathematical model has been validated that it not only expressed the relationship of movement synthesis for commonly spiral surface’s forming movement, but also depicted new spiral surface to be required or named through changing parameters.

Dynamic Modeling and Simulation of Salient Pole Synchronous Motor

2013 ◽  
Vol 392 ◽  
pp. 439-445
Author(s):  
Chao Shang ◽  
Zhi Fu Jiang ◽  
Jin Ru Gong
Keyword(s):  
Mathematical Model ◽  
Modeling And Simulation ◽  
Dynamic Modeling ◽  
Computer Control ◽  
Synchronous Motor ◽  
Salient Pole ◽  
Current Voltage ◽  
Three Phase ◽  
The Relationship ◽  
Simplified Mathematical Model

Aimed at salient pole machine synchronous motor, the relationship between the current, voltage, flux and torque were analyzed quantitatively, the simplified mathematical model based on abc three-phase variables was established, and it was converted into the model under d/q coordinates which is easily for computer control, finally, it is simulated by Matlab/Simulink.

Study on High Frequency Hydraulic Exciter Based on Rotary Valve Control

2012 ◽  
Vol 490-495 ◽  
pp. 1441-1445 ◽  
Author(s):  
Jian Zhuo Zhang ◽  
Li Zhe Guan ◽  
Kang Kang Li
Keyword(s):  
Mathematical Model ◽  
High Frequency ◽  
Rotary Valve ◽  
Exciting Frequency ◽  
Working Principle ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Valve Control

A kind of hydraulic exciter based on rotary valve control was studied in this paper, the composition of the exciter and its working principle were introduced, and the mathematical model of the system was established. The characters of the system were simulated using MATLAB. From the results of the simulation, we get the relationship of the amplitude of Vibration oil cylinder between the system’s pressure and the exciting frequency. The results can provide theoretical bases to design the hydraulic exciter.

Shaping Law and Motion Design in NC-ECM under Effect of Twiste Angle

2011 ◽  
Vol 128-129 ◽  
pp. 1010-1014
Author(s):  
Rui Wu ◽  
Dan Wen Zhang ◽  
Juan Sun
Keyword(s):  
Mathematical Model ◽  
Electrochemical Machining ◽  
Experimental Results ◽  
Working Face ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Motion Design

The twiste angle has a great effect on shaping law and stability of Numerical Controlled Electrochemical Machining (NC-ECM) process. In order to avoid the disadvantages caused by twiste angle, a methode of study shaping law by dispersing cathode working face in NC-ECM was proposed, and a mathematical model of the shaping law with the effects of twiste angle has been established in this paper. The mathematical model disclosed the relationship of twiste angle β, feeding velocity vf and thickness of removal material h in NC-ECM. Theoretical and experimental results show the the mathematical model of shaping law described in this paper can be considered as a useful reference and is helpful for the analysis of the NC-ECM and general ECM process.

Investigation on Silicon-Glass Electrostatic Bonding Time Experiment

2011 ◽  
Vol 483 ◽  
pp. 78-82
Author(s):  
Xiao Wei Liu ◽  
Jia Lu Tang ◽  
Rong Yan Chuai ◽  
Hai Feng Zhang ◽  
Xi Lian Wang
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Bonding Process ◽  
Bonding Time ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Electrostatic Bonding

In this paper, we make a detail analysis of some factors, which affects the electrostatic bonding process. According to the electrical properties of glass, combined with the principle of electrostatic bonding, we analysed the relationship of critical bonding time, voltage and temperature as well as the factors which affect electrostatic bonding. Then we come up with the mathematical model of the intensity and temperature of electrostatic bonding. In accordance with the above-mentioned formula and the experimental data, we can get the following conclusions: the intensity of electrostatic bonding is much greater between 280°C to 370°C; the best temperature for this bonding is about 350°C; however, when the temperature is below 280°C,the intensity of electrostatic bonding is lower due to the great impact of particles under low temperature; but when the temperature is higher than 370°C,the mismatch of coefficient of thermal expansion of silicon and glass gets larger, then as a result, the intensity of this bonding has a significant decrease with the increasing of temperature.

Effect of cutting width on the optimum size of bars and boards when cutting sawlogs with sawing three bars of equal thickness and four pairs of side boards

10.12737/4517 ◽  
2014 ◽  
Vol 4 (2) ◽  
pp. 128-135 ◽  
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimality Criterion ◽  
Constraint Equations ◽  
First Pass ◽  
Method Of Lagrange Multipliers ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Equal Thickness

There is a task of cutting optimization of sawlogs considering the width of cut. Output of sawn timber produced after the first pass of cutting sawlogs is chosen as optimality criterion. The objective function is represented as the sum of the cross-section of bars and planks. Such a mathematical model of the objective function establishes a relationship between size of bars and planks. Constraint equations represent the relationship of sawlogs diameter with the size of bars and boards, as well as the width of the cut. To solve the mathematical model the method of Lagrange multipliers is used.

Behavior of Localized Bottom Bulge in Aboveground Oil Storage Tanks Under Liquid Pressure

2001 ◽  
Vol 124 (1) ◽  
pp. 59-65
Author(s):  
Shoichi Yoshida
Keyword(s):  
Plastic Strain ◽  
Plate Thickness ◽  
Deformation Analysis ◽  
Bottom Plate ◽  
Storage Tanks ◽  
Liquid Pressure ◽  
Element Analysis ◽  
Oil Storage ◽  
Relationship Of ◽  
The Relationship

The bottom plate of aboveground oil storage tanks can bulge, separating from the foundation due to welding deformation. When such a bulge is subjected to liquid pressure, it deforms continuously to make contact with the foundation from the edge, and the remaining area of the bulge decreases with increasing liquid pressure. As a result, the deformation is extremely localized and plastic strain occurs at the bulge. This paper presents a plane strain finite element analysis for the evaluation of localized bottom bulges in aboveground oil storage tanks. Load-incremental, elastic-plastic large deformation analysis is carried out considering the bottom plate contact with the foundation. The relationship of the plastic strain at the bulged bottom plate to the liquid pressure is discussed together with the deformation of the bulge. As a result, the bottom plate thickness has a significant effect on the deformation, but the bulged height does not. After the bulged center makes contact with the foundation, the stress and strain do not increase with increasing liquid pressure. In addition, the permissible bulged profile specified by API Standard 653 elastically deforms to make contact with the foundation under low liquid pressure.

Simplified Model for the Seismic Performance of Unanchored Liquid Storage Tanks

2015 ◽  
Author(s):  
Maria Vathi ◽  
Spyros A. Karamanos
Keyword(s):  
Bottom Plate ◽  
Storage Tanks ◽  
Mass System ◽  
Aspect Ratios ◽  
Liquid Storage ◽  
Stress And Deformation ◽  
Cylindrical Tanks ◽  
Welded Connection ◽  
Simplified Modeling ◽  
Different Levels

Ground-supported unanchored liquid-storage cylindrical tanks, when subjected to strong seismic loading may exhibit uplifting of their bottom plate, which has significant effects on their dynamic behavior and strength. Those effects mainly concern: (a) the increase of axial (meridional) compression at the tank base, resulting in premature buckling in the form of elephant’s foot and (b) the significant plastic deformation at the vicinity of the welded connection between the tank shell and the bottom plate that may cause failure of the welded connection due to fracture and fatigue. The present study focuses on base uplifting mechanics and tank performance with respect to the shell/plate welded connection through a numerical two-step methodology: (1) a detailed finite element shell model of the tank for incremental static analysis, capable of describing the state of stress and deformation at different levels of loading and (2) a simplified modeling of the tank as a spring-mass system for dynamic analysis, enhanced by a nonlinear spring at its base to account for the effects of uplifting. Two cylindrical liquid storage tanks of different aspect ratios are modeled and analyzed in terms of local performance of the welded connection. The results are aimed at better understanding of tank uplifting mechanics and motivating possible amendments in existing seismic design provisions.

Numerical Investigation on Critical Submerged Depth During Draining From Cylindrical Tanks

2016 ◽  
Author(s):  
Liu Shi-wen ◽  
Zhou Jie ◽  
Huang Wei ◽  
Cheng Xiang
Keyword(s):  
Froude Number ◽  
Diameter Ratio ◽  
Nuclear Engineering ◽  
Initial Water ◽  
Design Work ◽  
Liquid Storage ◽  
Liquid Storage Tank ◽  
Cylindrical Tanks ◽  
Engineering Practices ◽  
Strong Vortex

Gas ingestion arises from free surface dip during draining from liquid storage tank does serious damage to the nuclear engineering practices, which should be considered in the design work. In this article, numerical simulations of transient process of draining from cylindrical tanks have been conducted with volume-of-fluid (VOF) method, by using the commercial CFD code FLUENT14.5. The relation between critical submerged depth and the Froude number has been investigated, then the influence of different factors on critical submerged depth also has been discussed. The results show that the Jain’s empirical formula are available to estimate the critical submerged depth flow with weak vortex in the condition of high diameter ratio and high initial water level. Moreover, the initial strong vortex significantly increase the critical submerged depth, while the surface tension has pretty small effects on the critical submerged depth when the Froude number is large.

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