Quantification of Saint-Venant's principle for a general prismatic member

A higher order beam model for thin-walled structures with in-plane rigid cross-sections

“…(30) represents a quadratic eigenvalue problem, being k and u 0 the eigenvalue and the corresponding eigenvector, respectively. The solution (28) was already considered in Toupin [49] for plane elasticity problems and in Goetschel [20] for the threedimensional structural behaviour of beams with a solid cross-section in order to provide a framework for the quantification of the Saint-Venant principle; in fact, the real part of the exponent parameter k is identified as the inverse of the decay length associated with higher order effects.…”

“…(i) The quantification of the Saint-Venant principle, as defined by Toupin [49] and Goetschel [20], provides a framework for developing a beam theory since it allows to represent the three-dimensional continuum mechanics in terms of the cross-section higher order modes (i.e., effects with a decaying behaviour). The higher order effects of a thinwalled beam model were obtained in Giavotto et al [19], Bauchau [2], Morandinia [32], Genoese [12], Ferradi [17,18] and cast within the framework of a geometrically exact beam theory in Genoese [14,15].…”

Laminated Composite Plates and Shells

“…Thus, the state space equation of the non-circular cylindrical shell can be derived by means of the process described in the previous sections. The solution of the materials, extensive work has been done either analytically (Klemm and Little, 1970) or numerically (Goetschel and Hu, 1985;Stephen and Wang, 1996). For elastic hollow cylinders, Stephen and Wang (1992) obtained an analytical solution , by which exact decay rates can be found in the context of three-dimensional considerations.…”

A method of analysis for end and transitional effects in anisotropic cylinders

“…This eigenproblem can be reduced to first-order form, from which it is possible to see that both real and complex eigendata are admissible -representing the possibility of both exponential and sinusoidal decays. Numerical data by this approach have been reported by Huang and Dong (1984), Dong and Huang (1985), Goetschel and Hu (1985), Kazic and Dong (1990) and Lin et al (2001), for a variety of problems related to orthotropic and anisotropic strips and circular cylinders as well as for general cross-sections. Inverse decay lengths have also been determined analytically from a transcendental equation of a boundary-value problem -see, Johnson and Little (1965) and Little and Childs (1967) for data on isotropic semi-infinite strips and circular cylinders, respectively.…”