Numerical analysis of shell and spatial structures

Since the advent of the computer into the engineering field, the application of the numerical methods to the solution of engineering problems has grown very rapidly. Among the different computer methods of structural analysis the Finite Element (FEM) has been predominantly used. Shells and space structures are very attractive and have been constructed to solve a large variety of functional problems (roofs, industrial building, aqueducts, reservoirs, footings etc). In this type of structures aesthetics, structural efficiency and concept play a very important role. This class of structures can be divided into three main groups, namely continuous (concrete) shells, space frames and tension (fabric, pneumatic, cable etc )structures. In the following only the current applications of the FEM to the analysis of continuous shell structures will be discussed. However, some of the comments on this class of shells can be also applied to some extend to the others, but obviously specific computational problems will be restricted to the continuous shells. Different aspects, such as, the type of elements,input-output computational techniques etc, of the analysis of shells by the FEM will be described below. Clearly, the improvements and developments occurring in general for the FEM since its first appearance in the fifties have had a significative impact on the particular class of structures under discussion.

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.

I.A.S.S. Symposium on Practical Aspects in the Computation on Shell and Spatial Structures

This work is the outcome of the interest that the Board of Executives of the lASS showed on the papers presented at the lASS-Symposium in Osaka (1986)

Some examples of the simultaneous use of closed-form and numerical solutions in shell structural analysis

The computational advantages of the use of different approaches -numerical and analytical ones- to the analysis of different parts of the same shell structure are discussed. Examples of large size problems that can be reduced to those more suitable to be handled by a personal related axisyrometric finite elements, local unaxisymmetric shells, geometric quasi-regular shells, infinite elements and homogenization techniques are described

A consistent method of analysis of RC shell structures

In this paper some topics related to the design of reinforced concrete (RC) shells are addressed. The influence of the reinforcement layout on the service and ultimate behavior of the shell structure is commented. The well established methodology for dimensioning and verifying RC sections of beam structures is extended. In this way it is possible to treat within a unified procedure the design and verification of RC two dimensional structures, in particular membrane and shell structures. Realistic design situations as multiple steel farnilies and non orthogonal reinforcement layout can be handled. Finally, some examples and applications of the proposed methodology are presented.

The nature of shield abnormalities in the turtle shell / [by] Rainer Zangerl -- and Ralph G. Johnson --.

v.10:no.29(1957)

Direct evidence for modified solvent structure within the hydration shell of a hydrophobic amino acid.

Neutron scattering experiments are used to determine scattering profiles for aqueous solutions of hydrophobic and hydrophilic amino acid analogs. Solutions of hydrophobic solutes show a shift in the main diffraction peak to smaller angle as compared with pure water, whereas solutions of hydrophilic solutes do not. The same difference for solutions of hydrophobic and hydrophilic side chains is also predicted by molecular dynamics simulations. The neutron scattering curves of aqueous solutions of hydrophobic amino acids at room temperature are qualitatively similar to differences between the liquid molecular structure functions measured for ambient and supercooled water. The nonpolar solute-induced expansion of water structure reported here is also complementary to recent neutron experiments where compression of aqueous solvent structure has been observed at high salt concentration.