Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

Abstract

In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. e effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. is paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

Dynamic Analysis of the Musical Triangles—Experimental and Numerical Approaches

“…Transient dynamic response analysis is the most general method of calculating the forced dynamic response. The purpose of such an analysis is to determine the behavior of a structure subjected to an excitation that varies over time [20][21][22][23][24][25]. Transient excitation is explicitly defined in the time domain.…”

“…Taking into account the equation of motion {P(t)} (2) and ignoring temporarily damping, Equation ( 3) is obtained [21][22][23][24][25]:…”

“…Since the matrices of mass and modal stiffness are diagonal matrices and have no off-diagonal terms, the equations of motion are uncoupled and can be written as a set of systems with a single degree of freedom (6) [21][22][23][24][25]:…”

“…In this study, the experimentally determined structural damping was introduced in the transient analysis, taking into account the dominant frequency at which the damping is active [21][22][23][24][25]. Thus, the structural damping is converted to viscous damping and the modal viscous damping matrix B qq is obtained based on relation (8):…”

Improved Strategy of Two-Node Curved Beam Element Based on the Same Beam’s Nodes Information

“…In order to calculate the curvature information of the curved beam element, a common strategy is to develop higher order curved beam element to calculate the curvature information in the inner regions of the beam [12][13][14][15][16][17]. Taking the three-node curved beam element as an example, adapted in the professional finite element software ANSYS (C3-ANSYS), three nodes in an element do not have to be colinear, and the curvature information in the element can be calculated by nodes interpolation method.…”