Solution of a boundary-value problem which arises in determining the state of stress of solid rock

1970 ◽  
Vol 6 (4) ◽  
pp. 377-379
Author(s):  
B. V. Vlasenko ◽  
L. G. Guzevskii
Keyword(s):  
Boundary Value Problem ◽  
Solid Rock ◽  
Boundary Value ◽  
The State ◽  
State Of Stress

The state of stress in solid rock with a horizontal working with stowing

1973 ◽  
Vol 9 (3) ◽  
pp. 227-235 ◽  
Author(s):  
Yu V. Nemirovskii ◽  
V. E. Mirenkov
Keyword(s):  
Solid Rock ◽  
The State ◽  
State Of Stress ◽  
Horizontal Working

On the Stress Analysis of Cylindrically Wound Packages: The Case of a Warp Beam

1976 ◽  
Vol 46 (6) ◽  
pp. 453-459 ◽  
Author(s):  
Subhash K. Batra ◽  
Danny S. Lee ◽  
Stanley Backer
Keyword(s):  
Experimental Data ◽  
Boundary Value Problem ◽  
Thermal Effects ◽  
The State ◽  
Polymeric Films ◽  
Prolonged Storage ◽  
Anisotropic Models ◽  
State Of Stress ◽  
Anisotropy Parameters ◽  
Cylindrically Anisotropic

The state of stress in a warp beam is investigated through continuum (isotropic and anisotropic) models. Beddoe's [2] model (cylindrically anisotropic) is found to give an acceptable description. The anisotropy parameters are estimated by comparing the calculated results with the experimental data. Influence of prolonged storage at higher temperatures (up to 130°F) on the barrel pressure and flange thrust are discussed. An auxiliary (boundary value) problem is formulated to account for these thermal effects; its solution gives results which are comparable to those observed experimentally. Means of estimating the mechanical and thermomechanical parameters of the system are discussed in some detail. The analyses can be adapted to model the state of stress in the cylindrically wound packaging of sheet-like material such as paper and polymeric films.

scholarly journals Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints

2021 ◽  
pp. 2009-2021
Author(s):  
Lamyaa H Ali ◽  
Jamil A. Al-Hawasy
Keyword(s):  
Optimal Control ◽  
Boundary Value Problem ◽  
State Vector ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
The State ◽  
Control Vector ◽  
Vector Solution ◽  
Solvability Theorem ◽  
Hyperbolic Boundary

The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient conditions" SCOs"), together denoted as NSCOs, for the optimality (OP) of the state constrained problem (SCP) are stated and proved.

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