Analytical Solutions of Out-of-Plane Problems for Infinite Elastic Bimaterials with a Circular Elastic Inclusion.

1995 ◽  
Vol 61 (592) ◽  
pp. 2663-2669
Author(s):  
Noriaki Sugisaka ◽  
Ken-ichi Hirashima
Keyword(s):  
Analytical Solutions ◽  
Elastic Inclusion ◽  
Out Of Plane ◽  
Circular Elastic Inclusion

Stresses in a Spherical Shell With a Circular Elastic Inclusion

1974 ◽  
Vol 96 (3) ◽  
pp. 228-233
Author(s):  
P. Prakash ◽  
K. P. Rao
Keyword(s):  
Differential Equations ◽  
Spherical Shell ◽  
Elastic Inclusion ◽  
Circular Inclusion ◽  
Shallow Spherical Shell ◽  
Spherical Shells ◽  
Hankel Functions ◽  
Circular Elastic Inclusion ◽  
Rigid Circular Inclusion

The problem of a circular elastic inclusion in a thin pressurized spherical shell is considered. Using Reissner’s differential equations governing the behavior of a thin shallow spherical shell, the solutions for the two regions are obtained in terms of Bessel and Hankel functions. Particular cases of a rigid circular inclusion free to move with the shell and a clamped rigid circular inclusion are also considered. Results are presented in nondimensional form which will greatly facilitate their use in the design of spherical shells containing a rigid or an elastic inclusion.

Dynamic Characteristics of Tsing Ma Suspension Bridge

1996 ◽  
Vol 1541 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Siu Kui Au ◽  
Neil Mickleborough ◽  
Paul N. Roschke
Keyword(s):  
Analytical Solutions ◽  
Bridge Deck ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Suspension Bridge ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Quantitative Results ◽  
Suspension Cable ◽  
Bending Modes

Numerical simulation was carried out to determine the dynamic properties of the Tsing Ma Suspension Bridge. Both the structure as a whole and individual subcomponents were modeled. Classical analytical solutions for simplified models from the available literature were compared with the results obtained from a finite-element code. Quantitative results for static deflection, natural frequencies, and mode shapes were compared with analytical solutions from linear theory. Out-of-plane modes were shown to be dominant. For in-plane antisymmetric and symmetric bending modes, in which the suspension cable and bridge deck vibrate in the same direction, the natural frequency of the main span of the bridge is determined to be approximately equal to the square root of the sum of the squares of the frequencies of the cable and bridge deck.

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.

Refined First-Order Shear Deformation Theory Models for Composite Laminates

2003 ◽  
Vol 70 (3) ◽  
pp. 381-390 ◽  
Author(s):  
F. Auricchio ◽  
E. Sacco
Keyword(s):  
Shear Deformation ◽  
Analytical Solutions ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Quadratic Functions ◽  
Shear Stresses ◽  
Stress Profile ◽  
First Order ◽  
Out Of Plane

In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stresses can be derived without post-processing procedures. Some numerical applications are presented in order to verify the effectiveness of the proposed formulations. In particular, analytical solutions obtained using the developed models are compared with the exact three-dimensional solution, with other classical laminate analytical solutions and with finite element results. Finally, we note that the proposed formulations may represent a rational base for the development of effective finite elements for composite laminates.

On Partially Debonded Circular Inclusions in Finite Plane Elastostatics of Harmonic Materials

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
X. Wang ◽  
E. Pan
Keyword(s):  
Mixed Boundary ◽  
Elastic Inclusion ◽  
Mixed Boundary Conditions ◽  
Finite Plane ◽  
Full Field ◽  
Square Root Singularity ◽  
Circular Elastic Inclusion ◽  
Plane Elastostatics ◽  
External Loads ◽  
Finite Plane Deformations

We investigate a partially debonded circular elastic inclusion embedded in a particular class of harmonic materials by using the complex variable method under finite plane-strain deformations. A complete (or full-field) solution is derived. It is observed that the stresses in general exhibit oscillatory singularities near the two tips of the arc shaped interface crack. Particularly the traditional inverse square root singularity for stresses is observed when the asymptotic behavior of the harmonic materials obeys a constitutive restriction proposed by Knowles and Sternberg (1975, “On the Singularity Induced by Certain Mixed Boundary Conditions in Linearized and Nonlinear Elastostatics,” Int. J. Solids Struct., 11, pp. 1173–1201). It is also found that the number of admissible states under finite plane deformations for given external loads can be two, one, or even zero.

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