Application of the Elasticity Solution to Linear Sandwich Beam, Plate and Shell Analyses

Abstract

The elasticity solution for sandwich structural elements like beams, orthotropic plates and shells is considered to yield exact results for deflections, stresses, frequencies, vibration modes, local (faces), and global (beam, plate, shell) buckling modes and related instability loads for certain boundary and loading conditions, as well as for constant material properties and small deflections. This approach therefore appears to be useful to be applied to such sandwich structures as benchmark analysis with the aim to calibrate Finite Elements computation models especially for thin face layers, thick cores, and local loading or face layer stability investigations. This paper compiles related experiences and describes some difficulties involved and provides some results, which can be used as benchmark references. The analytical solution remains applicable for unequal faces and any thickness relation, while F.E. calculations become very tedious if very thin faces are to be considered. It appears therefore desirable to be able to refer to a standard solution even if special boundary conditions only, like simply supported edges, are treated.

A Mechanics of Materials/Fracture Mechanics Analysis of Core Shear Failure in Foam Core Composite Sandwich Beams

“…The book by Vinson [1] summarizes many of the relevant analytical solutions for such behavior. Mathematically rigorous theory of elasticity solutions, such as the ones by Frostig et al [2] and Meyer-Piening [3], and finite element models, such as the one by Cho and Averill [4], are particularly useful for 3D elastic stress analyses and benchmarking but may not be suitable for quick estimates of fracture. As indicated by the experiments of Daniel et al [5] and Steeves and Fleck [6], the analysis of fracture of such structures is more complicated because of multiple possible failure modes such as core shear, face sheet wrinkling, face sheet microbuckling, and face sheet indentation.…”

Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment

“…A sample of selected papers published in recent years is given in the list of references, which review the state of the art and provide numerous cross-references on the subject, see Birman (2002), Sisemore and Darvennes (2002), Sokolinsky et al (2002), Choi (2003), Nabarrete et al (2003), Bozhevolnaya and Sun (2004), Kapuria et al (2004), Meyer-Piening (2004), Plagianakos and Saravanos (2004), Ruzzene (2004), Sokolinsky et al (2004), Ganesan and Pradeep (2005), Hao and Rao (2005), Numayr and Qablan (2005), Yang and Qiao (2005) and . One of the main reasons for conducting research in this area is due to the fact that sandwich constructions offer designers a number of advantages of which, perhaps the most important one is the high strength to weight ratio.…”

Three-Dimensional Closed Form Solutions and ∞3Theories for Orthotropic Plates

“…The exact solution is obtained by finding the expressions for the displacements and stresses which satisfy all equations (indefinite equilibrium, Hooke's law, geometric relations) and boundary conditions. There are many approaches to the determination of the exact solution [17][18][19][20][21][22][23][24][25].…”

“…All the theories based on the Generalized Unified Formulation will be compared against the exact solution obtained by solving the elasticity equations [16][17][18][19][20][21][22][23][24][25]. The three-dimensional solution used in this paper is an extension to the orthotropic case of a previous author's work [16].…”