title: Closed-form solution for a cantilevered sectorial plate subjected to a tip concentrated force.
abstract: A closed-form solution is presented for a cantilevered sectorial plate subjected to a tip concentrated force. Since the particular solution for this problem was not found in the literature, it is derived here. Deflections from the total solution (particular plus homogeneous solutions) are compared to those from a finite element analysis and are found to be in excellent agreement, producing an error within approximately 0.08 %. Normalized closed-form deflections and slopes at the fixed support, resulting from an approximate enforcement of the boundary conditions there, deviate from zero by <0.08 %. Finally, the total closed-form solutions for a cantilevered sectorial plate subjected to independent applications of a tip concentrated force, a tip bending moment, and a tip twisting moment, are compiled.
authors.affiliation: Zapata Incorporated, 6302 Fairview Road, Suite 600, Charlotte, NC 28210 USA.
authors.forename: Carl W
authors.initials: CW
authors.lastname: Christy
authors.affiliation: Department of Civil and Environmental Engineering, UNC Charlotte, 9201 University City Blvd., Charlotte, NC 28223 USA.
authors.forename: David C
authors.initials: DC
authors.lastname: Weggel
authors.affiliation: The William States Lee College of Engineering, UNC Charlotte, 9201 University City Blvd., Charlotte, NC 28223 USA.
authors.forename: R E
authors.initials: RE
authors.lastname: Smelser
keywords: Bending moment; Cantilever; Concentrated force; Sectorial plate; Twisting moment