Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

Stability and free vibration analysis of tapered sandwich columns with functionally graded core and flexible connections

Abstract: In this study, the buckling and free vibration behavior of tapered functionally graded material (FGM) sandwich columns is explored. The connections are considered to be semi-rigid. The core material is functionally graded along the beam depth according to the simple power law form. Euler–Bernoulli beam theory and the Ritz method will be employed to derive the governing equations. Legendre polynomials are chosen as auxiliary functions. After reducing the order of Euler’s buckling equation, an Emden–Fowler differential equation will be obtained. To reach a closed-form solution, the flexural rigidity of the column will be approximated with an exponential function by enforcing least-squares method. Non-dimensional natural frequencies and critical buckling loads will be presented for various cross-sectional types. The effects of FGM power, taper ratio, and spring rigidities on the critical buckling loads, and natural frequencies will be also investigated. Numerical results for various boundary conditions and configurations reveal the high accuracy of authors’ scheme.

Instability of Tapered Thin‐Walled Beams of Generic Section

Abstract: Buckling loads and natural frequencies and the corresponding modal shapes and forms for thin‐walled tapered beams of open sections are examined using the finite‐element method. A tapered thin‐walled bar finite element with seven degrees of freedom at each node is adopted. In the virtual work formulation, the updated Lagrangian approach is adopted in which the effect of geometric nonlinearity is considered. A rigorous expression for strains based on membrane theory of shells is considered. The flexural stiffness matrix, geometric stiffness matrix, and consistent mass matrices are derived in a companion paper. The convergence and accuracy of the method is tested based on other numerical results. Using the present theory, one is able to investigate various torsional and flexural static and dynamic instability problems. Examples are presented and comparisons are made with the existing solutions.