Finite Element Multiple-Mode Approach to Nonlinear Free Vibrations of Shallow Shells

Non-linear Vibrations of Deep Cylindrical Shells by thep-Version Finite Element Method

“…In the particular case of cylindrical shells defined by Eq. (1) ∂w i (x, y) ∂y is, evidently, zero, so only the restriction ∂w i (x, y) ∂x 2 1 remains. The strain field is of the following form [10] …”

“…However, the h-version of this method -which is the more common version and where refined models are obtained by increasing the number of elements over the domain -is constrained by a high computational cost (references [1,2], for example).…”

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

“…However, nonlinear curved and/or anisotropic structural analysis can result in a solution that will not be upper-bounded by a linear analysis. 13,14 Figure 10 and Figure 11 present linear and nonlinear vertical root mean square (RMS) displacement results at the mid-span and quarter-span locations, respectively. It is clearly seen that for the shallow arch analyzed herein, the displacements at both selected locations obtained from the nonlinear analysis will exceed the results obtained form the linear calculations.…”

“…Thus, the focus of this study is to extend the authors' previous work using an indirect stiffness evaluation approach to determine the effect of modal basis selection on the response of structures with shallow curvature. It is known that such structures may exhibit not only a hardening but also a softening type of nonlinearity 13,14 which may be non-conservative relative to a linear solution.…”

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

“…Thus, the focus of this study is to extend the authors' previous work using an indirect stiffness evaluation approach to determine the effect of modal basis selection on the response of structures with shallow curvature. It is known that such structures may exhibit not only a hardening but also a softening type of nonlinearity 13,14 which may be non-conservative relative to a linear solution. For planar configurations, the linear bending and membrane responses are uncoupled.…”