Bi-directional functionally graded thin-walled non-prismatic Euler beams of generic open/closed cross section Part II: Static, stability and free vibration studies

• Published in: Thin-walled structures 2019-08, Vol.141, p.646-674
• Main Authors: Rajasekaran, Sundaramoorthy, Khaniki, Hossein Bakhshi
• Format: Article
• Language: English
• Subjects: Eigen value; Eigen vector; Functionally graded; Natural frequency; Open and closed sections; Tapered beam; Thin-walled beam; Torsional buckling
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2019.02.005

In the current study, deflections, buckling loads, natural frequencies and the corresponding mode shapes and forms for BDFG thin-walled tapered beams of generic open/closed/open-closed sections are examined using the finite element method. A tapered thin-walled beam finite element with the seven degrees of freedom at each node is investigated. A rigorous expression for strains based on the membrane theory of shells is considered. The flexural stiffness matrix, geometric stiffness matrix and the consistent mass matrices are developed in a companion paper. Using the present theory, one is able to investigate various torsional, flexural static and dynamic systems. Examples are presented and comparisons are made with the existing available literature. With the modifications of axial, coupled and bending rigidities one will be able to investigate composite beams with fibre reinforced composite laminates. •Static, buckling and vibration behavior for BDFG tapered beams of thin-walled sections is investigated.•Different material and geometric variations are considered in this paper.•Considering any reference point and axes passing through it, BDFG tapered Euler thin-walled beam analysis becomes simpler.•Different types of thin-walled both open/closed cross sections are considered.•The validity and the adequacy of the theory are verified by many examples through comparisons made by other investigators.