CALCULATION OF THE STABILITY OF THE SIMPLE STATICALLY INDETERMINATE BEAM SYSTEMS ENERGY METHOD

2016 ◽  
pp. 8-10
Author(s):  
V. N. Mozgunov ◽  
A. A. Shirshov
Keyword(s):  
Energy Method ◽  
The Stability

The Energy Solutions for the Stability of Tower Crane

2012 ◽  
Vol 170-173 ◽  
pp. 3159-3165
Author(s):  
Ming Xin Huang ◽  
Jian Ping Xu ◽  
Jian Guo Wu
Keyword(s):  
Energy Method ◽  
Buckling Load ◽  
Tower Crane ◽  
The Stability ◽  
Design And Construction

The energy method is used to solve the buckling load of tower crane. It can conclude the effect law on the stability of different section parameters of tower crane and thus provides some references for the design and construction of tower crane.

scholarly journals Improving the energy method for calculating beams with a narrow rectangular section on the side buckling

2020 ◽  
Vol 164 ◽  
pp. 02033
Author(s):  
Serdar Yazyev ◽  
Anastasia Lapina ◽  
Ivan Zotov ◽  
Anton Chepurnenko ◽  
Irina Doronkina
Keyword(s):  
Analytical Solution ◽  
Total Energy ◽  
Energy Method ◽  
Strain Energy ◽  
Vertical Displacement ◽  
Center Of Gravity ◽  
Rectangular Section ◽  
Minimum Total Energy ◽  
The Stability ◽  
External Forces

We propose an improved version of the energy method in calculating rectangular beams for the stability of a flat bending shape. The essence of this variant of the method is to use the principle of the minimum total energy instead of the condition for the equality of the potential strain energy and the work of external forces. This version of the method makes it easy to obtain a numerical-analytical solution for any number of members of series. The solution of the problem for a pivotally supported beam is presented taking into account the vertical displacement of the load relative to the center of gravity.

Lp ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES

2004 ◽  
Vol 01 (03) ◽  
pp. 581-603 ◽  
Author(s):  
SHUICHI KAWASHIMA ◽  
SHINYA NISHIBATA ◽  
MASATAKA NISHIKAWA
Keyword(s):  
Conservation Laws ◽  
Energy Method ◽  
Optimal Convergence Rate ◽  
Estimates Of Solutions ◽  
Interpolation Inequalities ◽  
Optimal Decay ◽  
Viscous Conservation Laws ◽  
The Cauchy Problem ◽  
Whole Space ◽  
The Stability

We introduce a new Lp energy method for multi-dimensional viscous conservation laws. Our energy method is useful enough to derive the optimal decay estimates of solutions in the W1,p space for the Cauchy problem. It is also applicable to the problem for the stability of planar waves in the whole space or in the half space, and gives the optimal convergence rate toward the planar waves as time goes to infinity. This energy method makes use of several special interpolation inequalities.

Precise Stability Analysis of Stepped Telescopic Booms and Practical Algorithm

2013 ◽  
Vol 395-396 ◽  
pp. 871-876
Author(s):  
Liang Du ◽  
Peng Lan ◽  
Nian Li Lu
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Energy Method ◽  
Cross Sectional ◽  
Component Method ◽  
Practical Algorithm ◽  
The Stability ◽  
Precise Expression ◽  
Constant Section

To analyze the stability of stepped telescopic booms accurately, using vertical and horizontal bending theory, this paper established the deflection differential equations of stepped column model of arbitrary sectioned telescopic boom, the stability were analyzed, and obtained the precise expression of the buckling characteristic equation; Took certain seven-sectioned telescopic booms as example, by comparing the results with ANSYS, the accuracy of the equations deduced in this paper was verified. Presented the equivalent component method for the stability analysis of multi-stepped column, the equivalent cross-sectional moment of inertia was deduced by energy method, thus the stability of stepped column equivalent to that of constant section component. By comparing the results with exact value, the precision of equivalent component method was verified which was convenient for stability analysis of telescopic boom.

Research on Stability of Pressure Bars under the Function of Lateral Centralism Load

2011 ◽  
Vol 378-379 ◽  
pp. 297-301
Author(s):  
Zi Lin Li ◽  
Yu Bin Gao ◽  
Xue Song Wang
Keyword(s):  
Energy Method ◽  
Reference Value ◽  
Critical Force ◽  
Important Thing ◽  
Foreign Literature ◽  
Sufficient Stability ◽  
The Stability ◽  
First Time

To ensure the pressure bars to work safely and reliably, the most important thing is that the bars should possess sufficient stability. The previous massive domestic and foreign literature is just about the instability of the pressure bars under the function of longitudinal critical force, the research on the instability under action of the lateral critical force is seldom. So the research on the stability under the function of the lateral critical force is of great importance. This paper deduces the formula of the lateral critical force with the energy method for the first time when the pressure bars is in the condition of instability, and the formula has good reference value for the research on instability of the pressure bars under the lateral critical force.

scholarly journals Non-modal instability in plane Couette flow of a power-law fluid

2011 ◽  
Vol 676 ◽  
pp. 145-171 ◽  
Author(s):  
R. LIU ◽  
Q. S. LIU
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Energy Method ◽  
Stability Theory ◽  
Initial Conditions ◽  
Shear Thinning ◽  
Plane Couette Flow ◽  
Power Law Fluid ◽  
The Stability ◽  
Thinning Effect

In this paper, we study the linear stability of a plane Couette flow of a power-law fluid. The influence of shear-thinning effect on the stability is investigated using the classical eigenvalue analysis, the energy method and the non-modal stability theory. For the plane Couette flow, there is no stratification of viscosity. Thus, for the stability problem the stress tensor is anisotropic aligned with the strain rate perturbation. The results of the eigenvalue analysis and the energy method show that the shear-thinning effect is destabilizing. We focus on the effect of non-Newtonian viscosity on the transition from laminar flow towards turbulence in the framework of non-modal stability theory. Response to external excitations and initial conditions has been studied by examining the ε-pseudospectrum and the transient energy growth. For both Newtonian and non-Newtonian fluids, it is found that there can be a rather large transient growth even though the linear operator of the Couette flow has no unstable eigenvalue. The results show that shear-thinning significantly increases the amplitude of response to external excitations and initial conditions.

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.

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