Thin‐Walled Curved Beams. II: Analytical Solutions for Buckling of Arches

1994 ◽  
Vol 120 (10) ◽  
pp. 2102-2125 ◽  
Author(s):  
Young J. Kang ◽  
Chai H. Yoo
Keyword(s):  
Analytical Solutions ◽  
Curved Beams ◽  
Thin Walled

Pretwisted Curved Beams of Thin-Walled Open Section

1972 ◽  
Vol 39 (3) ◽  
pp. 779-785 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
Highway Bridges ◽  
Major Effect ◽  
Curved Beams ◽  
Open Section ◽  
Straight Beam ◽  
Thin Walled ◽  
Bending Modes ◽  
Axes Of Symmetry

Equations of motion are derived for coupled extension, flexure, and torsion of pretwisted curved bars of thin-walled, open section. The derivation is based on energy principles and includes inertia terms. The major effect of initial pretwist is to allow coupling of all possible beam deformation modes; however, if the bar is straight and has two axes of symmetry, pretwist causes coupling only between the two bending modes, and between extension and torsion. The governing equations are presented in first-order form, and a numerical technique is suggested for the case of space varying pretwist. It is suggested that these equations may form the basis for a simplified study of the effect of superelevation on the static and dynamic response of curved highway bridges. Finally, a simple straight beam with uniform pretwist is studied to compare effects of pretwist and restrained torsion in a thin-walled beam of open section.

Static Analysis of Curved Beams with Clamped-Clamped Ends under Thermo Load

2011 ◽  
Vol 117-119 ◽  
pp. 1543-1546
Author(s):  
Xiao Fei Li ◽  
Chun Yi Cui ◽  
De Hai Yu
Keyword(s):  
Thermal Expansion ◽  
Static Analysis ◽  
Cross Section ◽  
Analytical Solutions ◽  
Virtual Work ◽  
Curved Beams ◽  
Curved Bridges ◽  
Internal Forces ◽  
The Cross ◽  
Scientific Base

Based on the principle of thermal expansion and theory of virtual work, a class of equations for in-plane displacements at three freedom direction and internal forces in the cross-section of statically indeterminate curved beams under thermo load are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. The analytical solutions obtained in this paper would provide a scientific base for further study and design of the curved bridges.

Exact Solutions of Dynamic Characteristics for Curved Beams with Pinned-Pinned Ends

2013 ◽  
Vol 405-408 ◽  
pp. 702-705
Author(s):  
Xiao Fei Li ◽  
Wei Ming Yan ◽  
Hao Xiang He
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Analytic Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. Basing on the stiffness matrix of statically indeterminate curved beams at three freedom direction, the dynamic characteristics are derived explicitly. The analytic method of dynamic characteristics for curved beam performed in this paper would provide a scientific base for further study and design of the curved bridges.

Hinges and Curved Lamina Emergent Torsional Joints in Cylindrical Developable Mechanisms

2020 ◽  
Author(s):  
Kendall Seymour ◽  
Pietro Bilancia ◽  
Spencer Magleby ◽  
Larry Howell
Keyword(s):  
Cylindrical Surface ◽  
Small Scale ◽  
Membrane Thickness ◽  
Cylinder Wall ◽  
Small Length ◽  
Curved Beams ◽  
Modeling Assumption ◽  
Thin Walled

Abstract Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved Lamina Emergent Torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.

Lateral Buckling of Cantilevered Circular Arches Under Various End Moments

2020 ◽  
Vol 20 (07) ◽  
pp. 2071005
Author(s):  
Y. B. Yang ◽  
Y. Z. Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Curved Beams ◽  
Lateral Buckling ◽  
Circular Arch ◽  
Out Of Plane ◽  
The Moment

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

Sign in / Sign up

Export Citation Format

Share Document