On the Stability of Sizing Optimization Problems for a Class of Nonlinearly Elastic Materials

2001 ◽  
Vol 44 (3) ◽  
pp. 227-244
Author(s):  
C. Stangl
2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.


2021 ◽  
pp. 29-35
Author(s):  
Ilya A. Gulyaev Gulyaev ◽  
Evgeniy P. Ronnov

. A method of stability analysis for combined ship (oil carrier/platform ship type) at the stage of design study is presented. It should be noted that not all of ship’s main seaworthiness and operational characteristics are the result of a simple addition of the characteristics of an oil carrier and a platform ship. Their mutual influence takes place, which should be taken into account when analysing the stability in the multivariant optimization problems of internal and external design of such ships. This leads to the requirement to adjust the known methods of stability analysis at the initial stages of ship design, which was the purpose of the present work and its originality. Taking into account the multivariance of the task and the hull design type, the stability assessment will be carried out through the analysis of the metacentric height extreme value on the assumption that the requirements of Russian River Register for admissible heeling angle at static wind effect are met. In order to account for nonlinearity of static stability curve when inclining up to the angles of deck immersion into water and emergence of bilge, it is suggested to apply an approximate method of metacentric radius determination. The proposed method of combined ship stability assessment is recommended to apply at the stage of justification and analysis of ship’s key elements as a limitation in the problems of mathematical modeling of optimization of such type of ships. The method allows to exclude from further consideration at the design study stage the possible options that do not meet the requirements of seaworthiness.


2011 ◽  
Vol 16 (8) ◽  
pp. 833-871 ◽  
Author(s):  
Joseph McMahon ◽  
Alain Goriely ◽  
Michael Tabor

Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed.


Author(s):  
Ali A. Al-Arbo ◽  
Rana Z. Al-Kawaz

<span>This paper proposes a new spectral conjugate gradient (SCG) approach for solving unregulated nonlinear optimization problems. Our approach proposes Using Wolfe's rapid line scan to adjust the standard conjugate descent (CD) algorithm. A new spectral parameter is a mixture of new gradient and old search path. The path provided by the modified method provides a path of descent for the solution of objective functions. The updated method fits the traditional CD method if the line check is correct. The stability and global convergence properties of the current new SCG are technically obtained from applying certain well-known and recent mild assumptions. We test our approach with eight recently published CD and SCG methods on 55 optimization research issues from the CUTE library. The suggested and all other algorithms included in our experimental research were implemented in FORTRAN language with double precision arithmetic and all experiments were conducted on a PC with 8 GB ram Processor Intel Core i7. The results indicate that our proposed solution outperforms recently reported algorithms by processing and performing fewer iterations in a shorter time.</span>


Sign in / Sign up

Export Citation Format

Share Document