# Optimal Design of Structures

22/03/2016

## Introduction

Most CAE software suppliers announce: “Our software helps you to make an optimal design of your structures”. It this achieved in reality?

Broadly speaking if one claims optimisation of structures, in fact only a few chosen structural parts are optimized. A design engineer searches for the minimal size of the cross-section satisfying the design code, he/she tries to find the minimum number of bolts needed in a specific steel connection, he/she is searching for the minimum required area of reinforcement steel in a concrete beam. All structural parts are designed optimally, yet it does not mean that the whole structure is optimized for instance from the point of view of cost of materials, time of construction, price of labour, etc.

An optimal design of a structure is found when many design variants are tried out and compared. Everybody will agree, but how many times it is really done in the construction industry? Normally the designer works under the pressure of the client and there is hardly any time to study variants.

A typical example concerns a reinforced concrete beam. First the dimensions of the cross-section are preselected, then the internal forces are calculated and the reinforcement is designed, optimally of course. Yet who plays a little more with the depth and width of the beam to find an optimal price of the whole beam, which is composed out of the price of concrete and the price of steel?

Almost everybody is able to do it with existing software tools, it is only the question of testing of number of variants, comparing them and finding the most suitable one. In fact, this methodology may be realistic for small projects, but certainly not for real big projects. An experienced designer will certainly get closer to an optimum than a young starter.

## Optimisation of systems

The research on optimisation is mainly lead by automotive and aerospace industries. The emphasis is mainly on the computational fluid dynamics domain and structural optimisation area, especially on the shape optimisation.

There are many mathematical methods, which could answer the needs of the construction and building industry. Normally the system has to be described with a number of parameters. Then one has to set the target of the optimisation – what is the goal, what should be minimized or maximized?

And it is required to be able to calculate this goal from any set of parameters. If one does so, then one has defined what is normally “goal function” or “price function”.

Once a set of parameters and the goal function are defined, one can use standard mathematical optimisation methods, it does not matter if we optimise the weight of a space shuttle or the traffic in the streets.

## Five conditions for the optimal design of structures

Having powerful software tools for the design of structural parts and the mathematical methods for optimisation of systems being clear, why then is the optimisation of structures not widely used? The current CAE software systems are not equipped well enough for the structural optimisation. Which necessary functions should be integrated? Five main conditions have to be fulfilled.

Condition 1

Functions for optimal design of specific structural members like a steel beam, concrete beam, steel connection, foundation block, etc. Usually the minimal dimensions, size or number are searched for. The member must satisfy the criteria of the appropriate code.

Condition 2

There must be a possibility to parameterise the structure. The designer has to decide, what is fixed in the structure and what can be changed – spans, depths, dimensions of cross-sections, thickness of plates and walls, loads ... Each feature which can vary must be able to be described by one independent parameter. Other dimensions can be dependant on parameters, creating an intelligent parametric structural model.

Condition 3

There must be a possibility to define the goal function. It can be the weight of required structural steel, the volume of concrete, the weight of reinforcement, but it can also be maximal displacement or anything else. The ideal situation is if the system is able to calculate one overall value like the price.

Condition 4

The software system must be able to evaluate the goal function for the specific set of parameters. It means that a function, which is able to read the set parameters and return a goal value, must be available.

Condition 5

The optimisation solver is needed. This is a tool, which generates the different sets of parameters, calculates the goal function, and finally proposes the optimal set of parameters. With a CAE system equipped with all such functions, the way to the optimisation is wide open.