On the existence and uniqueness of a warpening function in the Elastic—plastic torsion of a cylindrical bar with multiply connected cross—section

1976 ◽  
pp. 328-342 ◽  
Author(s):  
C. Gerhardt
Keyword(s):  
Cross Section ◽  
Existence And Uniqueness ◽  
Multiply Connected ◽  
Elastic Plastic

Optimal Solutions for Nonhomogeneous Multiply-Connected Torsional Sections

1989 ◽  
Vol 111 (1) ◽  
pp. 87-93 ◽  
Author(s):  
A. Mioduchowski ◽  
M. G. Faulkner ◽  
B. Kim
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Boundary Value ◽  
Optimization Procedure ◽  
Second Order ◽  
External Boundary ◽  
Optimal Solutions ◽  
Torsion Problem ◽  
Multiply Connected

Optimization of a second-order multiply-connected inhomogeneous boundary-value problem was considered in terms of elastic torsion. External boundary and material proportions are the applied constraints in finding optimal internal configurations of the cross section. The optimization procedure is based on the numerical simulation of the membrane analogy and the results obtained indicate that the procedure is usable as an engineering tool. Optimal solutions are obtained for some representative cases of the torsion problem and they are presented in the form of tables and figures.

scholarly journals Rate of deformation in the cross section of a spatially curved rod with various assumptions

2021 ◽  
Vol 18 (3) ◽  
pp. 76-83
Author(s):  
Yu. L. Rutman ◽  
◽  
V. A. Meleshko ◽  
Keyword(s):  
Cross Section ◽  
Deformation Rate ◽  
Kinematic Parameters ◽  
Elastic Plastic ◽  
Tangential Stiffness ◽  
The Cross ◽  
Curved Rod

The article considers incremental relations connecting the changes in the kinematic parameters of the rod cross section with the deformation rate. These relations allow assessing the deformation rate on the elemental areas of a spatially curved rod, as well as considering the distortion of cross-section in its plane due to shear and torsion. Assessment of such relations between deformation rates and the rates of kinematic parameters allows developing the method of nonlinear calculation of rod systems based on integral expressions. Subsequently, these relations will be used for assessing the tangential stiffness of the rod element cross-section subjected to elastic-plastic calculation.

Response and Stability of Square Tubes Under Bending

1997 ◽  
Vol 64 (3) ◽  
pp. 649-657 ◽  
Author(s):  
S. P. Vaze ◽  
E. Corona
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Thickness Ratio ◽  
Pure Bending ◽  
Steel Tubes ◽  
Elastic Plastic ◽  
Plastic Steel

This paper addresses the response and stability of elastic-plastic steel tubes with square cross section under pure bending. An analytical model with sufficiently nonlinear kinematics to capture the development of ripples in the compression flange was developed. the results indicate that collapse of such tubes is imperfection sensitive for tubes with “high” height-to-thickness ratio (h/t), but the sensitivity decreases as h/t decreases. Experimentally, the tubes collapse due to a limit moment instability which is followed by the formation of a kink on the compression flange of the tubes. The limit moment and the development of the kink are captured well by the analytical model.

Elastic-Plastic Torque Analysis of Notched Cross-Section Bars Using the Finite Difference Method

2008 ◽  
Vol 385-387 ◽  
pp. 869-872 ◽  
Author(s):  
Hui Peng Liu ◽  
Xiang Rong Fu ◽  
Song Cen ◽  
Xiu Gen Jiang ◽  
Jin San Ju ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Cross Section ◽  
Finite Differences ◽  
Intensity Factors ◽  
Elastic Plastic ◽  
Numerical Tests ◽  
Finite Differences Method ◽  
New Strategy ◽  
Torque Analysis ◽  
The Finite Difference Method

A new strategy of finite differences method is proposed for analysis of notched cross-section bars under elastic-plastic torsion. Relation curves of the elastic-plastic torque responding with different positions, angles and lengths of the notches in one section are obtained by numerical tests. It can be seen that these relation curves exhibit obvious nonlinearity. Meanwhile, the stress intensity factors can also be easily calculated by utilizing the results of above finite differences method. It provides an effective way for solving such elastic-plastic fracture mechanics problem.

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