# Problem Definitions for Scilab Applications

# Objectives

The objective of this session is to solicit from the participants, simple problems from their respective fields of interest, that are well suited for solving using Scilab. The contributions may consist of the following:

- A brief and concise problem statement
- Some concepts, theory and mathematics required to solve the problem
- Scilab solution in the form of scripts, functions, numerical examples, solutions from known theory and comparison of results obtained from Scilab with those obtained from theory

# Sample Problems from Structural Engineering

You are invited to add ascomments to this post, the brief problem statements. Explaining the theory may involve more effort, in which case you can write it up in a document, upload it to the web (Google Docs, your blog etc.) and provide the link in the comment. You can do the same with the solution too.

To get you started, I will list a few problems from structural engineering:

- Determine the principal stresses and principal planes in a three dimensional state of stress (Theory of elasticity).
- Develop a function to compute the least square polynomial fit for a set of recorded data, similar to the polyfit() function in Matlab. Function must return the coefficients of the polynomial of the specified degree.
- Determine the free vibration results (natural frequencies and corresponding mode shapes) of a multi-degree of freedom spring-mass system. Frequencies must be arranged in increasing order and columns of mode shape matrix must be rearranged depending on how the frequencies are sorted.
- Analysis of skeletal structures using truss and beam elements by the direct stiffness matrix method of structural analysis
- Analysis of continua by the Finite Element Method (I agree the problem is too big, but can you not make a beginning using the simplest elements?).
- Optimization of skeletal steel structures (such as trusses, domes, roof grids) designed as per the building code of your country.

Note that the above are not precise problem definitions and do not include theory, solution and code. The last few problems will involve considerable effort even for very simple features (as compared to existing commercial software tools).