The exact thick arch finite element

✍ Scribed by Przemysław Litewka; Jerzy Rakowski

• Book ID: 104268990
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 394 KB
• Volume: 68
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(98)00051-0

✦ Synopsis

The exact stiness matrix is derived for a curved beam element with constant curvature. The plane two-node six degree-of-freedom element is considered in which eects of ¯exural, axial and shear deformations are taken into account. The analytical shape functions describing radial and tangential displacements as well as cross-section rotations are found in the algebraic±trigonometric form. They contain the coupled in¯uences of shear and membrane eects. Based on these shape functions, using the strain energy formula, the stiness matrix for shear ¯exible and compressible arch element is formulated. Obviously, this element is completely free of shear and membrane locking eects. The advantage of the elaborated element is its applicability to any combination of geometrical properties of the arch structure, e.g. the depth±length ratio of element. In presented numerical examples the shear and membrane in¯uences on the displacements for various cases of boundary conditions and loading are investigated. The results coincide exactly with the analytical ones obtained for continuous arches.