Keywords:elasticity, shear modulus, stress analysis, integral equations
1 Complex potentials suggested by Muskhelishvili should be an analytic function (2). However, since the argument is involved in the second term of in Eq. (1), cannot be an analytic function. Therefore, in Eq. (1) is a wrong expression.
2 In the complex variable function method, the displacement components can be expressed as (2)
where G is the shear modulus of elasticity, is for the plane stress problem, is for the plane strain problem, and ν is the Poisson’s ratio, and and are two analytic functions.
Equation (4) reveals a rule that in a real displacement expression of plane elasticity, if the function after the elastic constant κ is the term after z in Eq. (4) should be
3 In Eq. (3) an indefinite integral is used to express the stress components. In the continuum medium of elastic body, the integral should be path-independent. Also, it is well known that if a function
is a path independent integral, the following condition must be satisfied:
X. H., and
On the Relation Between the L-integral and the Bueckner Work-Conjugate Integral,”
ASME J. Appl. Mech.,
Muskhelishvili, N. I., 1953, Some Basic Problems of Mathematical Theory of Elasticity, Noordhoof, Dordrecht, The Netherlands.
Copyright © 2002