Quasilinearization method for analytical solutions to nonlinear problems of solid mechanics: A plate with a central circular hole under the creep regime

2020 ◽  
Author(s):  
L. V. Stepanova ◽  
R. M. Zhabbarov
Keyword(s):  
Circular Hole ◽  
Analytical Solutions ◽  
Solid Mechanics ◽  
Nonlinear Problems ◽  
Quasilinearization Method ◽  
Creep Regime

scholarly journals QUAZILINEARIZATION METHOD FOR THE SOLUTION TO THE PROBLEM OF PLATE WITH THE CENTRAL CIRCULAR HOLE UNDER CREEP REGIME

2017 ◽  
Vol 23 (2) ◽  
pp. 44-50
Author(s):  
L. V. Stepanova ◽  
R. M. Zhabbarov
Keyword(s):  
Numerical Solution ◽  
Tangential Stress ◽  
Circular Hole ◽  
Infinite Plate ◽  
Nonlinear Problems ◽  
Internal Point ◽  
Approximation Solution ◽  
Maximum Value ◽  
Creep Regime

The approximation solution of the problem for an infinite plate with the circular hole under creep regime is obtained by the quazilinearization method. Four approximations of the solution of the nonlinear problems are found. It is shown that with increasing of the number of approximations the solution converges to the limit numerical solution. It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is also shown that quazilinearization method is an effective method for nonlinear problems.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

Mechanics of Growing Solids: New Track in Mechanical Engineering

2014 ◽  
Author(s):  
Alexander V. Manzhirov
Keyword(s):  
Mathematical Theory ◽  
Solid Mechanics ◽  
Volcanic Rocks ◽  
Nonlinear Problems ◽  
Biological Tissues ◽  
Growth Processes ◽  
Continuous Growth ◽  
Engineering Sciences ◽  
Space Objects ◽  
Classical Boundary

A vast majority of objects around us arise from some growth processes. Many natural phenomena such as growth of biological tissues, glaciers, blocks of sedimentary and volcanic rocks, and space objects may serve as examples. Similar processes determine specific features of many industrial processes which include crystal growth, laser deposition, melt solidification, electrolytic formation, pyrolytic deposition, polymerization and concreting technologies. Recent researches indicates that growing solids exhibit properties dramatically different from those of conventional solids, and the classical solid mechanics cannot be used to model their behavior. The old approaches should be replaced by new ideas and methods of modern mechanics, mathematics, physics, and engineering sciences. Thus, there is a new track in solid mechanic that deals with the construction of adequate models for solid growth processes. The fundamentals of the mathematical theory of growing solids are under consideration. We focus on the surface growth when deposition of a new material occurs at the boundary of a growing solid. Two approaches are discussed. The first one deals with the direct formulation of the mathematical theory of continuous growth in the case of small deformations. The second one is designed for the solution of nonlinear problems in the case of finite deformations. It is based on the ideas of the theory of inhomogeneous solids and regards continuous growth as the limit case of discrete growth. The constitutive equations and boundary conditions for growing solids are presented. Non-classical boundary value problems are formulated. Methods for solving these problems are proposed.

Sign in / Sign up

Export Citation Format

Share Document