Recent results concerning the application of Lie transformation group methods to structural mechanics are presented. Focus is placed on the point Lie symmetries and conservation laws inherent to the Bernoulli–Euler and Timoshenko beam theories as well as to the Marguerrevon Kármán equations describing the large deflection of thin elastic shallow shells within the framework of the nonlinear Donn...

Geometrically nonlinear analysis of thin circular plates on Winkler elastic foundations has been studied in this paper. The nonlinear partial differential equations obtained from von Karman’s large deflection plate theory have been solved by using the discrete singular convolution (DSC) in the space domain and the harmonic differential quadrature (HDQ) method in the time domain.

A new two-step theory is investigated for predicting the deflection and slope of an entire structure using strain measurements at discrete locations. In the first step, a measured strain is fitted using a piecewise least-squares curve fitting method together with the cubic spline technique. These fitted strains are integrated twice to obtain deflection data along the fibers. In the second step,...

We compute the deflection angle for a light ray traveling in a flat ΛCDM cosmology which encounters a completely condensed mass region to second order inm/r0 and first order inm/r0×Λr 2 0.We find that the most significant correction to the Einstein angle occurs not because of the non-linear terms but instead because the condensed mass is embedded in an expanding cosmology. We predict a decrease...

With the aim of extending the use of integrated variational principles on fluid and deckplate to the large deflection analysis of floating roofs, this paper investigates the significance of theflexural and membrane components in the formulations of the deck plate. Applying integratedvariational principles on deck plate and fluid facilitate the treatment of the compatibility ofdeformation betwee...

In this research static deflection and free vibration of homogeneous nanobeams coated by a functionally graded (FG) layer is investigated according to the nonlocal elasticity theory. A higher order beam theory is used that does not need the shear correction factor. The equations of motion (equilibrium equations) are extracted by using Hamilton’s principle. The material properties are considered...