Sinniah Ilanko

The use of negative penalty functions in linear systems of equations

Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles.

Base Isolator of Vertical Seismic Vibration Using a Negative Stiffness Mechanism

A model of a base isolator for vertical seismic vibration is considered. It consists of a mass and two springs, one of which is a linear type and the other is of varying stiffness. It is assumed that the varying stiffness spring can be changed from positive to negative stiffness. The varying stiffness is accomplished by the horizontally placed springs which are also connected the vertical spring by rigid links providing geometric stiffness which is negative due to compression in the spring and the axial stiffness from the inclined links which decrease as their orientation approaches the horizontal direction. The numerical investigation shows that the force induced in the vertical spring becomes constant regardless of the displacement around half of the maximum contraction. The experiment also confirmed this force-displacement relationship. In the range of displacement, the force transmitted to an object supported by the isolator due to the ground motion can be limited. This mechanism offers a possible way to prevent an object from being damaged by excessive force during earthquakes.

Editorial to special issue of Computers & Structures

This special issue includes twenty-three extended, reviewed and revised papers originally presented at the Eleventh International Conference on Computational Structures Technology (CST2012) and the Eighth International Conference on Engineering Computational Technology (ECT2012) held concurrently in Dubrovnik, Croatia, 4–7 September 2012. The CST2012 Young Researcher Best Paper Prize was presented to Dr J.-W. Simon, of the RWTH Aachen University, Germany, for his paper “Limit States of Structures in n-dimensional Loading Spaces with Limited Kinematical Hardening”. The ECT2012 Young Researcher Best Paper Prize was presented to Dr L. Barbie, of CEA-Cadarache, France, for the paper “An Automatic Multilevel Refinement Technique based on Nested Local Meshes for Nonlinear Mechanics” by L. Barbie, I. Ramiere and F. Lebon. The CST2012 Prize Paper is the first paper included in this special issue; while the ECT2012 Prize paper is the second paper included in this issue. The standard of the papers considered for these prizes was very high and the conference editors wish to thank the members of the conference editorial board for their work in considering all the applicants

On the ‘Proof’ of Assumptions in the Basic Theories of Bending and Torsion

In the theory of beam bending, transverse sections of a beam are assumed to remain plane during bending. In torsion analysis, the radii of shafts of circular cross-sections are assumed to remain straight during twisting. Some popular textbooks present mathematical proofs for these statements. This article shows that these proofs are incorrect and that these statements should be treated as assumptions.