Determining Critical States of Equilibrium of Plates and Shells Under Initial Stress

1942 ◽  
Vol 9 (1) ◽  
pp. A27-A30
Author(s):  
H. Hencky
Keyword(s):  
Cylindrical Shell ◽  
Energy Method ◽  
Virtual Work ◽  
The Body ◽  
Principle Of Virtual Work ◽  
Practical Applications ◽  
Fundamental Knowledge ◽  
Plates And Shells ◽  
The Stability

Abstract The purpose of this paper is to show that Rayleigh’s energy method, used by Timoshenko for the determination of critical loads in plates and shells, is capable of an important generalization. The work involved is a direct continuation of the energy method of Timoshenko and is based on the principle of virtual work. According to this principle the variation of the work of the outer forces together with the variation of the kinetic energy is equal to the variation of the elastic energy stored up in the body. The author develops a series of formulas, by means of which the stability of a cylindrical shell under various conditions of stress may be determined. The practical applications of these formulas, requiring only a fundamental knowledge of the mathematics of engineering, are illustrated by suitable examples.

A Taxonomy to Aid in the Design of Complex Physical Activities for Older Adults

2017 ◽  
Vol 61 (1) ◽  
pp. 21-25
Author(s):  
Lyndsie M. Koon ◽  
Robert J. Brustad ◽  
Megan Babkes Stellino
Keyword(s):  
Physical Activity ◽  
Older Adults ◽  
Cognitive Function ◽  
Environmental Context ◽  
Physical Activities ◽  
The Body ◽  
Practical Applications ◽  
Aging Adults ◽  
The Stability ◽  
Positive Results

Physical activity participation is a non-pharmaceutical intervention that can be utilized to maintain and improve cognitive function in aging adults. Although simple physical activities yield positive results in regards to cognitive function, cognitively and motorically complex physical activities may have an even greater benefit on neuroplasticity for older adults. Commercially available products such as physical activity apps or exergames offer this population a means to engage in regular physical activity on their own. However, a taxonomy is necessary to help distinguish simpler physical activities from more complex physical activities. The taxonomy proposed in this paper carefully considers the following characteristics: the stability or transport of the body, object manipulation, intertrial variability, the environmental context and the reaction or to others. The dimensions of the taxonomy are operationally defined and practical applications are provided.

Determination of Bearing Reactions of Spatial Linkages and Manipulators

1990 ◽  
Vol 112 (2) ◽  
pp. 168-174 ◽  
Author(s):  
F. L. Litvin ◽  
J. Tan
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
System Of Equations ◽  
Principle Of Virtual Work ◽  
Simultaneous Solution ◽  
Combined Application ◽  
Spatial Linkages ◽  
Virtual Velocity ◽  
D'alembert's Principle

Application of D’Alembert’s principle for determination of dynamic bearing reactions in joints of spatial linkages and parallel manipulators needs the simultaneous solution of a large system of equations. The authors of this paper propose an approach that is a combined application of principle of virtual work and D’Alembert’s principle. The main advantages of the proposed approach are: (1) reduction of the number of equations that have to be solved simultaneously, and (2) simplification of the expressions for the relative virtual velocity. The proposed approach is illustrated with the example of a 7-bar linkage and its application is explained with the crank-slider linkage.

General Instability of a Ring-Stiffened, Circular Cylindrical Shell Under Hydrostatic Pressure

1957 ◽  
Vol 24 (2) ◽  
pp. 269-277
Author(s):  
S. R. Bodner
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Differential Equations ◽  
Energy Method ◽  
Circular Cylindrical Shell ◽  
Orthotropic Shell ◽  
Simple Expression ◽  
Isotropic Shell ◽  
Numerical Examples ◽  
The Stability

Abstract The general instability load of a ring-stiffened, circular cylindrical shell under hydrostatic pressure is determined by analyzing an equivalent orthotropic shell. A set of differential equations for the stability of an orthotropic shell is derived and solved for the case of a shell with simple end supports. The solution is presented in terms of parameters of the ring-stiffened, isotropic shell, and a relatively simple expression for the general instability load is obtained. Some numerical examples and graphs of results are presented. In addition, an energy-method solution to the problem is outlined, and the energy and displacement functions that could be used in carrying out a Rayleigh-Ritz approximation are indicated.

Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

On Dynamically Equivalent Force Systems and Their Application to the Balancing of a Broom or the Stability of a Shoe Box

2004 ◽  
Author(s):  
Just L. Herder ◽  
Arend L. Schwab
Keyword(s):  
Rigid Body ◽  
Center Of Mass ◽  
The Body ◽  
Resultant Force ◽  
Dynamic Equivalence ◽  
Force Systems ◽  
The Stability ◽  
Metacentric Height ◽  
The Given

The stability of a rigid body on which two forces are in equilibrium can be assessed intuitively. In more complex cases this is no longer true. This paper presents a general method to assess the stability of complex force systems, based on the notion of dynamic equivalence. A resultant force is considered dynamically equivalent to a given system of forces acting on a rigid body if the contributions to the stability of the body of both force systems are equal. It is shown that the dynamically equivalent resultant force of two given constant forces applies at the intersection of its line of action and the circle put up by the application points of the given forces and the intersection of their lines of action. The determination of the combined center of mass can be considered as a special case of this theorem. Two examples are provided that illustrate the significance of the proposed method. The first example considers the suspension of a body, by springs only, that is statically balanced for rotation about a virtual stationary point. The second example treats the roll stability of a ship, where the metacentric height is determined in a natural way.

Comparison of the Absorption and Destruction of the Lactone and Salt Form of Glucuronic Acid by Dogs

1956 ◽  
Vol 188 (1) ◽  
pp. 54-60
Author(s):  
F. A. Buckeridge ◽  
Smith Freeman
Keyword(s):  
Small Intestine ◽  
Plasma Concentration ◽  
Glucuronic Acid ◽  
The Body ◽  
Limiting Factor ◽  
Salt Form ◽  
Ph Values ◽  
Rate Of Absorption ◽  
The Stability

Comparative studies were made on the fate of d-glucuronolactone and d-glucuronate in dogs. The studies included: a) measurement of the rate of conversion of the lactone into the salt form at various ph values ranging from 2.0 to 7.4; b) measure of the rate of absorption from isolated loops of small intestine; c) determination of the blood plasma concentration in relation to intestinal absorption of the two forms of glucuronic acid in normal, Eck fistula and nephrectomized animals; d) the stability and magnitude of the plasma values were determined following the intravenous injection of the lactone or salt form of glucuronic acid into nephrectomized dogs. From the foregoing studies, it was determined that: a) glucuronolactone is rapidly converted into glucuronate at the ph of plasma; b) glucuronolactone is absorbed from the small intestine much more rapidly than is glucuronate; c) absorbed glucuronolactone is metabolized rapidly while glucuronate appears to be relatively inert in the body and to occupy a space similar to that of inulin. The limiting factor in the metabolism of glucuronolactone is the rate of its conversion into the salt form.

scholarly journals Nanofluid properties for forced convection heat transfer :a review

2015 ◽  
Vol 3 (1) ◽  
pp. 145 ◽  
Author(s):  
Mohsen Darabi ◽  
Reza Naeimi ◽  
Hamid Mohammadiun ◽  
Saeed Mortazavi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Base Fluid ◽  
Convection Heat Transfer ◽  
Theoretical Models ◽  
Transfer Coefficients ◽  
Practical Applications ◽  
Heat Transfer Coefficients ◽  
The Stability

<p>The thermal conductivity of nanofluids depends on various parameters, such as concentration, temperature, particle size, pH, shape, material, and possibly on the manufacturing process of the nanoparticles. Data on the viscosity of nanofluids, available in the literature, are very limited. Theoretical models for the determination of the thermal conductivity and viscosity of nanofluids have been pursued. Experiments with nanofluids indicate that they higher heat transfer coefficients than the base fluid. No significant increase in a pressure drop is reported with nanofluids, compared with values with the base fluid. However, the stability of nanofluids with regard to settlement/agglomeration, especially at higher concentrations, is still a problem for practical applications.</p>

Theoretical and FEM Research on Inelastic Displacement of Assembled Truss Bridge with Cable Reinforcement

2012 ◽  
Vol 178-181 ◽  
pp. 2038-2042
Author(s):  
Yin Zhi Zhou ◽  
Ke Bin Jiang ◽  
Yong Ding ◽  
Jian Kui Yang
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
The Self ◽  
Principle Of Virtual Work ◽  
Element Analysis ◽  
Inelastic Displacement ◽  
Prestressing Force ◽  
Truss Bridge ◽  
Theoretical Results

This paper presents theoretical and finite element investigations on inelastic displacement of assembled truss bridge with cable reinforcement (hereinafter referred to as ATCR). A method based on the Principle of virtual work for the determination of the inelastic displacement of ATCR is proposed. Finite element analysis was conducted on the specimen models using the ANSYS program, in order to obtain the inelastic displacement of ATCR and to compare with theoretical results. This study focuses on Bailey bridge under the self-weight load and prestressing force on cable. This paper analyzes various specimens to obtain inelastic displacement in different cases. The approximations of a relation between the inelastic displacement and prestressing force on cable are found. It can be seen that the method in this paper can both calculate the inelastic displacement of traditional truss and prestressed truss (ATCR). Based on both the theoretical and the finite element results, it can be concluded that the relation curve between inelastic displacement and prestressing force is stepwise.

scholarly journals The stability analysis of two-wheeled vehicle model

2018 ◽  
Vol 157 ◽  
pp. 01007 ◽  
Author(s):  
Juraj Gerlici ◽  
Vladimir Sakhno ◽  
Alla Yefymenko ◽  
Vladimir Verbitskii ◽  
Alexandr Kravchenko ◽  
...  
Keyword(s):  
Full Range ◽  
The Body ◽  
Complex Conjugate ◽  
Numerical Determination ◽  
Vehicle Model ◽  
Driving Mode ◽  
Wheeled Vehicle ◽  
The Stability ◽  
Disturbed Motion

This research investigates the stability of a two-wheeled vehicle model on the basis of numerical determination of full range of eigenvalues of a linear approximation matrix in the vicinity of the rectilinear driving mode. The received result was checked by numerical integration of the initial equations system of the disturbed motion of the model. The discrepancy of two research techniques is explained by the specialty of the considered mathematical model in which two pairs of complex conjugate eigenvalues close to each other are realized, that explains the emergence of standard derivations at calculating their numerical determination. The model is asymptotically stable in the range much wider than an operational interval (up to 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce additional resilient and damping elements between the trucks and the body in the design of the wheeled vehicle that will counteract the yaw mode of trucks.

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