Based on the general solution of piezoelectric media and the extended Cerruti solution for tangential point forces acted on the surface of transversely isotropic piezoelectric half-space (Ding and Chen, 2001), the ele...Based on the general solution of piezoelectric media and the extended Cerruti solution for tangential point forces acted on the surface of transversely isotropic piezoelectric half-space (Ding and Chen, 2001), the electro-elastic fields in a transversely isotropic piezoelectric half-space caused by a circular flat bonded punch under torsion loading, which is called Reissner-Sagoci problem, are evaluated by first evaluating the displacement functions within the contact region and then differentiating them. All the coupling electro-elastic fields are expressed by elementary functions and are convenient to be used. Numerical results are finally presented.展开更多
In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement comp...In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.展开更多
文摘Based on the general solution of piezoelectric media and the extended Cerruti solution for tangential point forces acted on the surface of transversely isotropic piezoelectric half-space (Ding and Chen, 2001), the electro-elastic fields in a transversely isotropic piezoelectric half-space caused by a circular flat bonded punch under torsion loading, which is called Reissner-Sagoci problem, are evaluated by first evaluating the displacement functions within the contact region and then differentiating them. All the coupling electro-elastic fields are expressed by elementary functions and are convenient to be used. Numerical results are finally presented.
文摘In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.
