TABLE OF CONTENTS FOR TR95-74

Part I : INTRODUCTION TO ALADDIN

1. Introduction to ALADDIN
   1. Problem Statement
   2. ALADDIN Components
   3. Scope of this Report

   Part II : MATRIX LIBRARY

2. Command Language for Quantity and Matrix Operations
   1. How to Start (and Stop) ALADDIN
   2. Format of General Command Language
   3. Physical Quantities
      1. Definition and Printing of Quantities
      2. Formatting of Quantity Output
      3. Quantity Arithmetic
      4. Making a Quantity Dimensionless
      5. Switching units On and Off
      6. Setting Units Type to US or SI
   4. Control of Program Flow
      1. Logical Operations
      2. Conditional Branching
      3. Looping and Stopping Commands33~
   5. Defintion and Printing of Matrices
      1. Definition of Small Matrices
      2. Builtin Functions for Allocation of Matrices
      3. Defintion of Matrices with Units
      4. Printing Matrices with Desired Units
   6. Matrix-to-Quantity-Conversion
   7. Basic Matrix Operations
      1. Retrieving the Dimensions of a Matrix
      2. Matrix Copy and Matrix Transpose
      3. Matrix Addition, Subtraction, and Multiplication
      4. Scaling a Matrix by a Quantity
      5. Euclidean Norm of Row/Column Vectors
      6. Minimum and Maximum Matrix Elements
      7. Substitutions/Extractions of Submatrices
   8. Solution of Linear Matrix Equations
      1. Solving [A]{x}={b}
      2. Matrix Inverse
   9. Matrix Eigenvalues and Eigenvectors
      1. The Generalised Symmetrix Eigenvalue Problem
      2. Numerical Example 1 : Buckling of Rod
      3. Numerical Example 2 : Vibration of Cantilever Beam
3. Construction of Numerical Algorithms
   1. Introduction
   2. Roots of Nonlinear Equations
      1. Newton-Raphson and Secant Algorithms
      2. Broyden-Fletcher-goldfarb-Shanno (BFGS) Algorithm
   3. Han-Powell Algorithm for Optimization
      1. Quadratic Programming (QP)
      2. Armijo Line Search Rule
      3. The BFGS update and Han-Powell method
4. Computational Methods for Dynamic Analysis of Structures
   1. Introduction
   2. Method of Newmark Integration
   3. Method of Modal Analysis

   PART III : FINITE ELEMENT LIBRARY

5. Finite Element Analysis Language
   1. Introduction
   2. Structure of Finite Element Input Files
   3. Problem Specification Parameters
   4. Adding Nodes and Finite Elements
   5. Material and Section Properties
   6. Boundary Conditions
   7. External Nodal Loads
   8. Stiffness, Mass and External Loading Matrices
   9. Internal Loads
   10. Design Rule Checking
   11. Library of Finite Elements
6. Input Files for Finite Element analysis Problems
   1. Linear Static Analysis
      1. Analysis of Five Story Moment Resistant Frame
      2. Three-Dimensional Analysis of Highway Bridge
   2. Time-History Analysis
   3. Modal Analysis of Five Story Steel Frame
   4. Modal Analysis of Simple L-Shaped Base-Isolated Building

   PART IV : ARCHITECTURE AND DESIGN

7. Data Types : Physical Quantity and Matrix Structures
   1. Introduction
   2. Physical Quantities
      1. Relationship between Quantity and Units
      2. US and SI unit Conversion
   3. Matrices
      1. Skyline Matrix Storage
      2. Units Buffers for Matrix Multiplication
      3. Units Buffers for Inverse Matrix
8. Architecture and Design of ALADDIN
   1. Introduction
   2. Program Modules and Key Data Structures
   3. Design and Implementation of Stack Machine
      1. Example of Machine Stack Execution
   4. Language Design and Implementation

   PART V : CONCLUSIONS AND FUTURE WORK

9. Conclusions and Future Work
   1. Conclusions
   2. Future Work