# Projects

## Introduction

In addition to RMA's commercial activities and projects, the company undertakes a range of internal projects which are aimed at the development of the company's expertise. Much of this work is prepared for publications typically as articles for the practising engineer.

### Case Studies Demonstrating Industrial Usage of Engineering Analysis & Simulation

### Convergence & Extrapolation for Practising Engineers

The idea that with mesh refinement a finite element model should converge to the appropriate theoretical mathematical model is one on which engineers rely. The theoretical notions of convergence are though not necessarily simple to grasp and although theoretical rates of convergence can be obtained, these are not always achieved in practical finite element models. This project will look at the nature of convergence using practical engineering examples. Methods for extrapolating from the results of a series of analyses using increasingly refined meshes towards a better approximation of the theoretical solution will be examined. The outcome of this work will be one/two articles which, it is hoped, will be accepted for publication in the NAFEMS Benchmark Magazine.

### Stone Landings

### Limit Analysis

Limit analysis is a direct approach to finding the plastic limit load for a structure or member. It adopts a rigid-perfectly plastic material model with a yield criterion appropriate for the material. There are two main approaches which appeal to the plasticity theorems. The upper bound approach seeks to find a collapse mechanism for which the plastic limit load is a minimum whereas the lower bound approach seeks to find a field of stress resultants for which the plastic limit load is a maximum. The upper bound method therefore converges from above the true value and is therefore potentially unsafe whilst the lower bound approach always provides a safe solution. RMA have developed software, Equilibrium Finite Elements (EFE) to provide lower bound solutions for plate bending problems in reinforced concrete (RC slabs) and metallic plates.

### Design against Burst of Rotating Discs

This project aims to improve the understanding of calculation of the burst speed of rotating discs and to provide updated guidance to engineers working in the field of, amongst others, turbomachinery design. The current approach is based on a 1944 study which found a correlation between the burst speed and the average hoop stress reaching the UTS of the material. Whilst it is fairly easy to demonstrate the error of this approach, it remains in use today albeit with knock-down factors to hopefully ensure that use of the formula remains safe.

### The NAFEMS Benchmark Challenge (Completed)

RMA acted as an Independent Technical Editor in a new NAFEMS initiative to increase the interaction between Benchmark Magazine and its readership. The initiative was called The NAFEMS Benchmark Challenge with the first challenge being published in October 2014. A Response to the Challenge appeared in the following issue of Benchmark and during the period between issues readers collaborated and sought clarification through the Challenge Blog at NAFEMS. The challenges are going to be published in booklets by NAFEMS covering the complete challenges, responses and additional useful information for each year that the challenge continues to run.

### Stress Trajectories

Stress trajectories or more accurately principal stress resultant trajectories are of great value to engineers practicing in the field of reinforced concrete. For plate membrane problems the trajectories assist the engineer in finding a strut and tie model whereas for plate bending problems the principal moment trajectories give direct design information regarding the reinforcement layout.

### Equilibrium Finite Element Analysis of a Shear Wall

This project was undertaken in 1996 to assist a final year student at Nottingham Trent University. High-fidelity equilibrating stresses are presented from a very coarse mesh of a shear wall.