ANALYTICAL BENDING SOLUTIONS OF ELASTICA WITH ONE END HELD WHILE THE OTHER END PORTION SLIDES ON A FRICTION SUPPORT

Treated herein is an elastica under a point load. One end of the elast ica is fully restrained against translation, and elastically restraine d against rotation, while the other end portion is allowed to slide ov er a friction support. The considered elastica problem belongs to the class of large-deflection beam problems with variable deformed are-len gths between the supports. To solve the governing nonlinear differenti al equation together with the boundary conditions, the elliptic integr al method has been used. The method yields closed-form solutions that are expressed in a set of transcendental equations in terms of ellipti c integrals. Using an iterative scheme, pertinent bending results are computed for different values of coefficient of friction, elastic rota tional spring constant and loading position, so that their effects may be examined. Also, these accurate solutions provide useful reference sources for checking the convergence, accuracy and validity of results obtained from numerical methods and software for large deflection bea m analysis. It is interesting to note that this class of elastica prob lem may have two equilibrium states; a stable one and an unstable one.