Transcript Advanced Structures.ppt

B8 Advanced Structures
Syllabus
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Finite Difference analysis & solution of linear
equations using relaxation methods
Finite element analysis,
Dynamic analysis of structures including
modal analysis and time-stepping algorithms
Variational calculus
Convergence criteria and error bounding
Module Learning Outcomes
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Identify the appropriate differential equations and boundary
conditions for analysing a range of structural analysis and
solid mechanics problems.
Implement the finite difference method to solve a range of
continuum problems.
Implement a basic beam-element finite element analysis.
Implement a basic variational-based finite element analysis.
Implement time-stepping algorithms and modal analysis
algorithms to analyse structural dynamic problems.
Detail the assumptions and limitations underlying their
analyses and quantify the errors/check for convergence.
Reading and Resources
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In addition to a series of purpose written notes that will be
used to support the course the following standard texts are
recommended reading:
The finite element method for engineers, K.H. Heubner and
E.A. Thornton, Wiley Inter-science, 1982
Structural Analysis: A Unified Classical and Matrix Approach:
Amin Ghali, Adam Neville, TG Brown: Spon, 1997
Theory of Vibration with Applications by William T. Thomson,
Taylor and Francis
Theory of Elasticity (McGraw-Hill Classic Textbook Reissue
Series) by S. P. Timoshenko and J.N. Goodier
Numerical Methods for Engineers by Steven C. Chapra and
Raymond P. Canale, McGraw-Hill
Beam Element FEA
The fundamental equation describing the stiffness method is,
S D   FR 
Where,
 [S] is the stiffness matrix, which is know
 {D} is the vector of unknown displacements
 {-FR} is the vector of fictitious restraining forces (For a simple
pin- jointed truss is the same at the applied loads F)
General Procedure
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I – Identify n d.o.f.’s
II – Calculate {FR} and AR m1
III – Build [S] and AU mn
IV – Solve [S]{D}=-{FR}
V – Calculate m structural
actions Am1  AR m1  AU mn  Dn1
Master flow-diagram
for a beam-element
finite element
analysis program
Input Structure Data
Element Matrices
Restraining Force Vector &
Element Action Matrices
Generate Global
Stiffness Matrix
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