A variational principle in a geometrically nonlinear theory of heterogeneous viscoelastic shells

2009 ◽  
Vol 45 (2) ◽  
pp. 159-164 ◽  
Author(s):  
R. Yu. Amenzadeh
Keyword(s):  
Variational Principle ◽  
Nonlinear Theory ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Theory ◽  
Viscoelastic Shells

On the Nonuniqueness of Solutions Obtained With Simplified Variational Principles

1996 ◽  
Vol 63 (3) ◽  
pp. 820-827 ◽  
Author(s):  
H. Mang ◽  
P. Helnwein ◽  
R. H. Gallagher
Keyword(s):  
Variational Principle ◽  
Lagrange Multipliers ◽  
Variational Principles ◽  
Boundary Value ◽  
Geometrically Nonlinear ◽  
Lagrange Equations ◽  
Geometrically Nonlinear Theory ◽  
Nonuniqueness Of Solutions ◽  
Uniqueness Of The Solution ◽  
Bending Of Beams

The attempt to satisfy subsidiary conditions in boundary value problems without additional independent unknowns in the form of Lagrange multipliers has led to the development of so-called “simplified variational principles.” They are based on using the Euler-Lagrange equations for the Lagrange multipliers to express the multipliers in terms of the original variables. It is shown that the conversion of a variational principle with subsidiary conditions to such a simplified variational principle may lead to the loss of uniqueness of the solution of a boundary value problem. A particularly simple form of the geometrically nonlinear theory of bending of beams is used as the vehicle for this proof. The development given in this paper is entirely analytical. Hence, the deficiencies of the investigated simplified variational principle are fundamental.

Incompatibility of Martensite Variant Clusters in Self-accommodation Microstructure in Ti-Ni-Pd High Temperature Shape Memory Alloy

2015 ◽  
Vol 1760 ◽  
Author(s):  
Takeshi Teramoto ◽  
Masaki Tahara ◽  
Hideki Hosoda ◽  
Tomonari Inamura
Keyword(s):  
High Temperature ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Habit Plane ◽  
Nonlinear Theory ◽  
Geometrically Nonlinear ◽  
Martensite Variant ◽  
Geometrically Nonlinear Theory ◽  
Electron Backscattering Diffraction ◽  
Diamond Cluster

ABSTRACTThe formation frequency of habit plane variant (HPV) clusters in Ni-25Pd-50Ti shape memory alloy was analyzed using electron backscattering diffraction (EBSD) on the basis of the geometrically nonlinear theory of martensite. Two types of cluster, diamond and wedge, were most commonly observed. The ratio of the formation frequency of the diamond to wedge clusters was approximately 1 : 3, whereas the rotation to keep the kinematic compatibility (KC) condition, θ *, was 3.9° and 0.0032°, respectively. The ratio of the formation frequency is quantified by the value of θ * which is an indicator of the incompatibility of the cluster. The origin of the diamond cluster is discussed based on the degree of incompatibility.

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