Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Ivo Senjanović ◽  
Neven Alujević ◽  
Ivan Ćatipović ◽  
Damjan Čakmak ◽  
Nikola Vladimir ◽  
...  
Keyword(s):  
Strain Energy ◽  
Ritz Method ◽  
Double Fourier Series ◽  
External Pressure ◽  
Normal Displacement ◽  
Toroidal Shell ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Buckling Stability

The energy approach is used to analyze the buckling stability of toroidal shells. A closed and an open toroidal shell, as well as a shell segment are considered. Linear strain energy and nonlinear strain energy due to a uniform external pressure are formulated. Variations of the in-surface and normal displacement components in the circumferential and meridional directions are assumed in the form of a double Fourier series. The eigenvalue problem for the determination of the critical pressure is formulated by the Rayleigh–Ritz method (RRM). The proposed procedure is evaluated by numerical examples: one for a closed and another one for a simply supported open toroidal shell. The obtained results are validated by a comparison with results obtained by the finite strip method (FSM) and the finite element method (FEM), which shows a very good agreement.

A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Ivo Senjanović ◽  
Ivan Áatipović ◽  
Neven Alujević ◽  
Damjan Čakmak ◽  
Nikola Vladimir
Keyword(s):  
Internal Pressure ◽  
Cross Sections ◽  
Stiffness Matrix ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Toroidal Shell ◽  
Beam Shape ◽  
Finite Strip ◽  
Finite Strip Method ◽  
Toroidal Shells

In this paper, a finite strip for vibration analysis of rotating toroidal shells subjected to internal pressure is developed. The expressions for strain and kinetic energies are formulated in a previous paper in which vibrations of a toroidal shell with a closed cross section are analyzed using the Rayleigh–Ritz method (RRM) and Fourier series. In this paper, however, the variation of displacements u, v, and w with the meridional coordinate is modeled through a discretization with a number of finite strips. The variation of the displacements with the circumferential coordinate is taken into account exactly by using simple sine and cosine functions of the circumferential coordinate. A unique argument nφ+ω t is used in order to be able to capture traveling modes due to the shell rotation. The finite strip properties, i.e., the stiffness matrix, the geometric stiffness matrix, and the mass matrices, are defined by employing bar and beam shape functions, and by minimizing the strain and kinetic energies. In order to improve the convergence of the results, also a strip of a higher-order is developed. The application of the finite strip method is illustrated in cases of toroidal shells with closed and open cross sections. The obtained results are compared with those determined by the RRM and the finite element method (FEM).

scholarly journals Determination of bearing capacity of steel thinwalled cold-formed structures using the example of centrally compressed struts

2019 ◽  
Vol 135 ◽  
pp. 03016
Author(s):  
Olga Umnova ◽  
Irina Giyasova
Keyword(s):  
Bearing Capacity ◽  
Direct Method ◽  
Finite Strip ◽  
Regulatory Documents ◽  
Strip Method ◽  
Minimum Value ◽  
Thin Walled Structures ◽  
Finite Strip Method ◽  
Thin Walled

Until 2017, there were no regulatory documents in Russia that allowed calculations of light steel thin-walled structures (LSTWSs), which hampered their use in construction. The paper compares various methods of calculating LSTWSs in compliance with Russian, European and American standards, and describes their features. The direct method of finding the strength of steel thin-walled profiles, developed by American scientists B. Schafer and T. Pekoz, is described. The method is based on the determination of the bearing capacity of a section according to the results of calculating critical forces for three forms of buckling. Using the CUFSM program developed by B. Schafer on the basis of the finite strip method, a centrally compressed strut from LSTWS was calculated; critical forces of three forms of buckling were determined, and profile bearing capacity was determined as the minimum value of three.

scholarly journals Determination of time-dependent strengths of salt pillars based on strain energy principle

2019 ◽  
Vol 29 (2) ◽  
pp. 273-279 ◽  
Author(s):  
Prapasiri Junthong ◽  
Supattra Khamrat ◽  
Suratwadee Sartkaew ◽  
Kittitep Fuenkajorn
Keyword(s):  
Strain Energy ◽  
Time Dependent ◽  
Energy Principle
Sign in / Sign up

Export Citation Format

Share Document