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Aladdin : a Computational Toolkit for Interactive Engineering Matrix And ALADDIN A COMPUTATIONAL TOOLKIT FOR INTERACTIVE ENGINEERING MATRIX AND FINITE ELEMENT ANALYSIS Mark Austin Xiaoguang Chen and WaneJang Lin Institute for Systems Research and Department of Civil Engineering University of Maryland College Park MD Novemb er Abstract This rep ort describ es Version of ALADDIN an interactive computational to olkit for the matrix and nite element analysis of engineering systems The ALADDIN package is designed around a language sp ecication that includes quantities with physical units branching constructs and lo oping constructs The basic language functionality is enhanced with external libraries of matrix and nite element functions ALADDINs problem solving capabilities are demonstrated via the solution to a series of matrix and numerical analysis problems ALADDIN is employed in the nite element analysis of two building structures and two highway bridge structures Contents I INTRODUCTION TO ALADDIN Intro duction to ALADDIN Problem Statement ALADDIN Comp onents Scop e of this Rep ort II MATRIX LIBRARY Command Language for Quantity and Matrix Op erations How to Start and Stop ALADDIN Format of General Command Language Physical Quantities Denition and Printing of Quantities Formatting of Quantity Output Quantity Arithmetic Making a Quantity Dimensionless Switching Units On and O Setting Units Typ e to US or SI Control of Program Flow Logical Op erations Conditional Branching Lo oping and Stopping Commands Denition and Printing of Matrices Denition of Small Matrices Builtin Functions for Allo cation of Matrices Denition of Matrices with Units Printing Matrices with Desired Units MatrixtoQuantity Conversion Basic Matrix Op erations Retrieving the Dimensions of a Matrix Matrix Copy and Matrix Transp ose Matrix Addition Subtraction and Multiplication Scaling a Matrix by a Quantity Euclidean Norm of RowColumn Vectors Minimum and Maximum Matrix Elements SubstitutionExtraction of Submatrices Solution of Linear Matrix Equations Solving A fxg fbg Matrix Inverse Matrix Eigenvalues and Eigenvectors Solving K M Numerical Example Buckling of Ro d Numerical Example Vibration of Cantilever Beam Construction of Numerical Algorithms Intro duction Ro ots of Nonlinear Equations NewtonRaphson and Secant Algorithms BroydenFletcherGoldfarbShanno BFGS Algorithm HanPowell Algorithm for Optimization Quadratic Programming QP Armijo Line Search Rule The BFGS up date and HanPowell metho d Computational Metho ds for Dynamic Analysis of Structures Intro duction Metho d of Newmark Integration Metho d of Mo dal Analysis III FINITE ELEMENT LIBRARY Finite Element Analysis Language Intro duction Structure of Finite Element Input Files Problem Sp ecication Parameters Adding No des and Finite Elements Material and Section Prop erties Boundary Conditions External No dal Loads Stiness Mass and External Loading Matrices Internal Loads Retrieving Information from ALADDIN Library of Finite Elements Input Files for Finite Element Analysis Problems Linear Static Analyses Analysis of Five Story Moment Resistant Frame Working Stress Design WSD of Simplied Bridge ThreeDimensional Analysis of Highway Bridge TimeHistory Analyses Mo dal Analysis of Five Story Steel Frame IV ARCHITECTURE AND DESIGN Data Typ es Physical Quantity and Matrix Data Structures Intro duction Physical Quantities Relationship b etween Quantity and Units US and SI Units Conversion Matrices Skyline Matrix Storage Units Buers for Matrix Multiplication Units Buers for Inverse Matrix Architecture and Design of ALADDIN Intro duction Program Mo dules and Key Data Structures Design and Implementation of Stack Machine Example of Machine Stack Execution Language Design and Implementation V CONCLUSIONS AND FUTURE WORK Conclusions and Future Work Conclusions Future Work Part I INTRODUCTION TO ALADDIN Chapter Intro duction to ALADDIN Problem Statement This rep ort describ es the development and capabilities of ALADDIN Version an interactive computational to olkit for the matrix and nite element analysis of engineering systems The current target application area for ALADDIN is design and analysis of traditional Civil Engineering structures such as highway bridges and earthquakeresistant buildings With literally hundreds of engineering analysis and opti mization computer programs having b een written in the past years see references for some examples a reader might rightfully ask who needs to write another engineering analysis package We resp ond to this challenge and motivate the short and longterm goals of this work by rst noting that during the past two decades computers have b een providing approximately more p ower p er dollar p er year Advances in computer hardware and software have allowed for the exploration of many new ideas and have b een a key catalyst in what has led to the maturing of computing as a discipline In the s computers were viewed primarly as machines for research engineers and scientists compared to to days standards computer memory was very exp ensive and central pro cessing units were slow Early versions of structural analysis and nite element computer programs such as ABAQUS ANSR and FEAP were written in the FORTRAN computer language and were develop ed with the goal of optimizing numerical andor instructional considerations alone These programs oered a restricted but well implemented set of numerical pro cedures for static structural analyses and linearnonlinear timehistory resp onse calculations And even though these early computer programs were not partic ularly easy to use practising engineers gradually adopted them b ecause they allowed for the analysis of new structural systems in a ways that were previously intractable During the past twenty years the use of computers in engineering has matured to the p oint where imp ortance is now placed on ease of use and a widearray of services b e ing made available to the engineering profession as a whole Computer programs written for engineering computations are exp ected to b e fast and accurate exible reliable and of course easy to use Whereas an engineer in the s might have b een satised by a computer program that provided numerical solutions to a very sp ecic engineering prob lem the same engineer to day might require the engineering analysis plus computational supp ort for design co de checking optimization interactive computer graphics network connectivity and so forth Many of the latter features are not a b ottleneck for getting the job done Rather features such as interactive computer graphics simply make the job of describing a problem and interpreting results easier the pathway from easeofuse to pro ductivity gains is well dened It is also well worth noting that computers once viewed as a to ol for computation alone are now seen as an indisp ensable to ol for computation and communications In fact the merging of computation and communications is mak ing fundamental changes to the way an engineer conducts hisher daytoday business activities Consider for example an engineer who has access to a high sp eed p ersonal computer with multimedia interfaces and global network connectivity and who happ ens to b e part of a geographically disp ersed development team The team memb ers can use the InternetEmail for daytoday communications to conduct engineering analyses at remote sites and to share designanalysis results among the team memb ers Clear com munication of engineering information among the team memb ers may b e of paramount imp ortance in determining the smo oth development of a pro ject The diculty in followingup on the ab ovementioned
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