Shell equations in terms of Günter's derivatives, derived by the Γ‐convergence

The dimensioning of an orthotropically stiffened cylindrical CFRP shell subjected to the introduction of concentrated axial loads using rapid analytical methods is presented. For stress calculation the shell equations are simplified by applying the semibending theory and integrated by employing the transfer matrix method. Analytical approaches are used for stability verification. The dimensioning considers required constraints in the force flux distribution, strength of the laminate, general instability, panel instability (from ring frame to ring frame) and local instability. The rapid analytical methods allow mass optimization. The final design is confirmed by detailed FE analysis. A comparison of the FE analysis with the analytical results is shown.

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From nonlinear to linearized elasticity via Γ-convergence: The case of multiwell energies satisfying weak coercivity conditions

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202515500013 ◽

2014 ◽

Vol 25 (01) ◽

pp. 1-38 ◽

Cited By ~ 7

Author(s):

V. Agostiniani ◽

T. Blass ◽

K. Koumatos

Keyword(s):

Coercivity Conditions ◽

Coercivity Condition ◽

Nematic Elastomers ◽

Linearized Elasticity ◽

Γ Convergence

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers.

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Buckling of a Circular Cylindrical Web-Stiffened Sandwich Shell Under Axial Compression

Journal of Ship Research ◽

10.5957/jsr.1974.18.1.55 ◽

1974 ◽

Vol 18 (01) ◽

pp. 55-61

Author(s):

Vincent Volpe ◽

Youl-Nan Chen ◽

Joseph Kempner

Keyword(s):

Axial Compression ◽

Large Deflection ◽

Single Layer ◽

Subsequent Development ◽

Buckling Load ◽

Sandwich Shell ◽

Cylindrical Sandwich Shell ◽

Axisymmetric Mode ◽

Shell Equations ◽

The Mathematical Model

A stability analysis of an infinitely long web-stiffened, circular cylindrical sandwich shell under uniform axial compression is presented. The formulation begins with the establishment of a set of suitable large-deflection shell equations that forms the basis for the subsequent development of the buckling equations. The mathematical model corresponds to two face layers that are considered as thin shells and a thick core that is capable of resisting both transverse shear and circumferential extension. The associated eigenvalue problem is solved. Results show that the lowest buckling load is associated with the axisymmetric mode and is less than one half the buckling load of an equivalent single-layer shell.

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Cylindrical Shells Under Line Load

Journal of Applied Mechanics ◽

10.1115/1.4011600 ◽

1957 ◽

Vol 24 (4) ◽

pp. 553-558

Author(s):

R. M. Cooper

Keyword(s):

Cylindrical Shell ◽

Radial Displacement ◽

Circular Cylindrical Shell ◽

Transverse Shear Deformation ◽

System Of Equations ◽

Principle Of Superposition ◽

Line Load ◽

Simply Supported ◽

Shell Equations ◽

Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

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