The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fo...The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bat is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 alpha is equal to 2 pi and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox ate obtained. Moreover, the modified classical solution which remains bounded as 2 alpha approaches 2 pi is provided.展开更多
文摘The problem of the curved bar subjected to an arbitrarily distributed loading on the surfaces r=a and r=b is sp!ved by using the method of complex functions and expanding the boundary conditions at r=a and r=b into Fourier series. Then another paradox in the two-dimensional theory of elasticity is discovered, i. e., the classical solution becomes infinite when the curved bat is subjected to a uniform loading or when the angle included between the two ends of the curved bar 2 alpha is equal to 2 pi and the curved bar is subjected to a sine or cosine loading. In this paper the paradox is resolved successfully and the solutions for the paradox ate obtained. Moreover, the modified classical solution which remains bounded as 2 alpha approaches 2 pi is provided.
