On complex potentials in two-dimensional linearized elasticity with couple stresses

1969 ◽  
Vol 8 (3-4) ◽  
pp. 304-322 ◽  
Author(s):  
V. K. Stokes ◽  
D. C. Leigh
Keyword(s):  
Complex Potentials ◽  
Two Dimensional ◽  
Couple Stresses ◽  
Linearized Elasticity

Some two-dimensional flows with couple stresses

2012 ◽  
Vol 85 (3) ◽  
pp. 649-654 ◽  
Author(s):  
M. Sajid ◽  
N. Ali ◽  
Z. Abbas ◽  
T. Javed ◽  
M. Imran
Keyword(s):  
Two Dimensional ◽  
Couple Stresses ◽  
Two Dimensional Flows

Complex dynamical invariants for two-dimensional complex potentials

Pramana ◽  
2012 ◽  
Vol 79 (2) ◽  
pp. 173-183 ◽  
Author(s):  
J S VIRDI ◽  
F CHAND ◽  
C N KUMAR ◽  
S C MISHRA
Keyword(s):  
Complex Potentials ◽  
Two Dimensional ◽  
Dynamical Invariants

scholarly journals Complex potentials in two-dimensional elasticity

1945 ◽  
Vol 184 (997) ◽  
pp. 129-179 ◽  
Keyword(s):  
Complex Variable ◽  
Body Force ◽  
Displacement Function ◽  
The Body ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Two Dimensional ◽  
Special Cases ◽  
Airy’S Stress Function

This paper gives an approach to two-dimensional isotropic elastic theory (plane strain and generalized plane stress) by means of the complex variable resulting in a very marked economy of effort in the investigation of such problems as contrasted with the usual method by means of Airy’s stress function and the allied displacement function. This is effected (i) by considering especially the transformation of two-dimensional stress; it emerges that the combinations xx + yy , xx — yy + 2 ixy are all-important in the treatment in terms of complex variables; (ii) by the introduction of two complex potentials Ω( z ), ω( z ) each a function of a single complex variable in terms of . which the displacements and stresses can be very simply expressed. Transformation of the cartesian combinations u + iv , xx + yy , xx — yy + 2 ixy to the orthogonal curvilinear combinations u ξ + iu n , ξξ + ηη, ξξ - ηη + 2iξη is simple and speedy. The nature of "the complex potentials is discussed, and the conditions that the solution for the displacements shall be physically admissible, i.e. single-valued or at most of the possible dislocational types, is found to relate the cyclic functions of the complex potentials. Formulae are found for the force and couple resultants at the origin z = 0 equivalent to the stresses round a closed circuit in the elastic material, and these also are found to relate the cyclic functions of the complex potentials. The body force has bhen supposed derivable from a particular body force potential which includes as special cases (i) the usual gravitational body force, (ii) the reversed mass accelerations or so-called ‘centrifugal’ body forces of steady rotation. The power of the complex variable method is exhibited by finding the appropriate complex potentials for a very wide variety of problems, and whilst the main object of the present paper has been to extend the wellknown usefulness of the complex variable method in non-viscous hydrodynamical theory to two-dimensional elasticity, solutions have been given to a number of new problems and corrections made to certain other previous solutions.

Transverse bending of infinite and semi-infinite thin elastic plates. I

1957 ◽  
Vol 53 (1) ◽  
pp. 248-255 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Boundary Condition ◽  
Complex Variable ◽  
Practical Importance ◽  
Complex Potentials ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Simply Supported ◽  
Physical Conditions ◽  
Transverse Bending ◽  
Thin Elastic Plates

In recent years several authors have treated the fundamental problems of two-dimensional statical elasticity for isotropic and aeolotropic materials by the use of functions of a complex variable; references are given at the end of (7). In this paper Stevenson's notation (8,9) is adopted. Dawoud (2) has expressed the continuity conditions across a curve between two differently loaded regions in terms of the complex potentials and particular integrals for the two regions. A form of the boundary condition defining certain types of boundary constraint, including the rigidly clamped and hinged boundaries, has been introduced by the author and Dawoud (1). The introduction of this boundary condition is of practical importance, since neither rigidly clamped nor simply supported conditions can be realized fully under actual physical conditions and thus any case met in practice must lie somewhere between these two limiting cases.

Solitons in Kerr media with two-dimensional non-parity-time-symmetric complex potentials

2021 ◽  
Vol 146 ◽  
pp. 110837
Author(s):  
Xing Zhu ◽  
Shangwen Liao ◽  
Zhen Cai ◽  
Yunli Qiu ◽  
Yingji He
Keyword(s):  
Complex Potentials ◽  
Two Dimensional ◽  
Kerr Media ◽  
Symmetric Complex
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