On the Identities for Elastostatic Fundamental Solution and Nonuniqueness of the Traction BIE Solution for Multiconnected Domains

نویسندگان

  • Y. J. Liu
  • W. Ye
  • Y. Deng
چکیده

In this paper, the four integral identities satisfied by the fundamental solution for elastostatic problems are reviewed and slightly different forms of the third and fourth identities are presented. Two new identities, namely the fifth and sixth identities, are derived. These integral identities can be used to develop weakly singular and nonsingular forms of the boundary integral equations (BIEs) for elastostatic problems. They can also be employed to show the nonuniqueness of the solution of the traction (hypersingular) BIE for an elastic body on a multiconnected domain. This nonuniqueness is shown in a general setting in this paper. It is shown that the displacement (singular) BIE does not allow any rigidbody displacement terms, while the traction BIE can have arbitrary rigid-body translation and rotation terms, in the BIE solutions on the edge of a hole or surface of a void. Therefore, the displacement solution from the traction BIE is not unique. A remedy to this nonuniqueness solution problem with the traction BIE is proposed by adopting a dual BIE formulation for problems with multiconnected domains. A few numerical examples using the 2D elastostatic boundary element method for domains with holes are presented to demonstrate the uniqueness properties of the displacement, traction and the dual BIE solutions for multiconnected domain problems. [DOI: 10.1115/1.4023640]

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Identities for the fundamental solution of thin plate bending problems and the nonuniqueness of the hypersingular BIE solution for multi-connected domains

Four integral identities for the fundamental solution of thin plate bending problems are presented in this paper. These identities can be derived by imposing rigid-body translation and rotation solutions to the two direct boundary integral equations (BIEs) for plate bending problems, or by integrating directly the governing equation for the fundamental solution. These integral identities can be...

متن کامل

A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems

A new fast multipole boundary element method (BEM) is presented in this paper for large-scale analysis of two-dimensional (2-D) elastostatic problems based on the direct boundary integral equation (BIE) formulation. In this new formulation, the fundamental solution for 2-D elasticity is written in a complex form using the two complex potential functions in 2-D elasticity. In this way, the multi...

متن کامل

A tangential differential operator applied to stress and traction boundary integral equations for plate bending including the shear deformation effect

Stress boundary integral equations (BIEs) are required in elastic or inelastic analyses of plate bending problems to obtain distributed shear, bending and twisting moments. Traction BIE, which is important to perform fracture analyses, is directly related to stress BIE. The collocation point position and the strategy to treat improper integrals are essential features studied in BIE for traction...

متن کامل

Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations

Some integral identities for the fttndamental solutions of potential and elastostatic problems are established in this paper. With these identities it is shown that the conventional boundary integral equation (BIE), which is generally expressed in terms of singularintegrals in the sense of the Cauchy principal value (CPV), and the derivative BIE, which is similarly expressed in terms of hypersi...

متن کامل

On the conventional boundary integral equation formulation for piezoelectric solids with defects or of thin shapes

In this paper, the conventional boundary integral equation (BIE) formulation for piezoelectric solids is revisited and the related issues are examined. The key relations employed in deriving the piezoelectric BIE, such as the generalized Green's identity (reciprocal work theorem) and integral identities for the piezoelectric fundamental solution, are established rigorously. A weakly singular fo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013