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Torsion of Truncated Hollow Spherical Elastic Body
234-240Views:138This paper deals with the torsion of a body of rotation whose shape is a truncated hollow sphere. The material of the truncated hollow sphere is isotropic, homogeneous and linearly elastic. To solve the torsion problem, the theory of torsion of shafts of varying circular cross section is used, which is introduced by Michell and Föppl. Analytical solution is given for the shearing stresses and displacements. A numerical example illustrates the application of the presented solution. The results of the presented numerical example can be used as a benchmark problem to verify the accuracy of the results computed by finite element simulations.
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An Analytical Solution for Static Problems of Cantilever Curved Beams with Variable Cross Sections
226-233Views:144This paper gives an analytical method to obtain the deformation of a cantilever curved beam. The curved beam considered has circular centre line and the thickness of the cross section in radial direction depends on the circumferential coordinate. The kinematics of the Euler-Bernoulli beam model is used to formulate of governing equations. The curved homogeneous and isotropic elastic beam is fixed at the one of the end cross section and on the other end cross section is subjected to concentrated forces and a couple. A numerical example illustrates the applications of the derived formulae.
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An Analytical Solution for the Two-Layered Composite Beam-Column with Interlayer Slip and Constant Axial Load
14-31Views:89The authors present an analytical solution for the two-layered composite beams with imperfect shear connections. The considered beam is simply supported at both ends. The beam is subjected to transverse and axial loads. The kinematic assumptions of the Euler-Bernoulli beam theory are used. The connection of the beam components is perfect in normal direction, but the axial displacement field may have jump. The shear axial force derived from the imperfect connection is proportional to the relative slip occurring between the layers. The determination of the analytical solution is based on the Fourier method. Two examples illustrate the application of the presented analytical method.
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Thermoelastic Problems of Multilayered Spherical Pressure Vessels Subjected to Axisymmetric Loading
106-115Views:134This paper deals with the linear thermoelastic analysis of functionally graded multilayered spherical bodies subjected to constant mechanical and thermal loading. The temperature field is arbitrary function of the radial coordinate, the material properties and the radial body force vary according to power law functions along the radius of the sphere. An analytical method is presented to calculate the displacements and stresses within the multilayered spherical body. The method is expanded to tackle the problem of spherical bodies made from radially graded materials with temperature dependent material properties. The results are compared to finite element simulations and other methods.
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On the Torsional Rigidity of Orthotropic Beams with Rectangular Cross Section
25-30Views:97The paper deals with the torsional rigidity of homogenous and orthotropic beam with rectangular cross
section. The torsional rigidity of the considered beam is defined in the framework of the Saint-Venant theory of
uniform torsion. Exact and approximate solutions are given to the determination of the torsional rigidity. The shape
of cross section is determined which gives maximum value of the torsional rigidity for a given cross-sectional area.
The dependence of torsional rigidity as a function of the ratio shear moduli of beam is also studied. -
The Influence of the Boundary Conditions on the Buckling of Thin-walled Cans during Manufacturing
41-50Views:93In this paper the effect of the boundary conditions on the stability of thin-walled aerosol cans under axial pressure is investigated. The main objective is to outline the main characteristics of this highly nonlinear mechanical problem and to present methods to simulate the buckling of cans with different boundary conditions. Due to the numerical difficulties coming from the contact between the can and different components of the machines, the effect of the different supports of the can is investigated on the crushing (or buckling) force at which the loss of stability occurs. The commercial finite element software Abaqus is used to solve the problems and to present the efficiency of FE codes in the design process of cans.
