Lesson Objectives
CEE 4100 – Computer Analysis of Structures – Spring 2012
Lesson 1: Introduction, Matrix Definition and Operations – Reading: A.1–A.2
• Define matrices and vectors and list matrix types
• Define and perform the matrix operations of:
– scalar multiplication,
– matrix addition and subtraction, and
– matrix multiplication.
• Solve a system of simultaneous equations using matrix calculations
• Calculate the determinant of a matrix and explain what it means
Lesson 2: Visual Basic Programming in Excel (CECIL)
• Create user-defined functions in Excel
Lesson 3: General Steps of FEM, Derivation of Bar (Truss) Element – Reading: 1.4,3.1–3.2
• Derive the bar (truss) element stiffness matrix from basic principles
• Assemble the global stiffness matrix
• Solve bar problems using the finite element method
Dr. Roberts Out of Town – Guest Speaker?
Lesson 4: Solving 2-D Trusses Using Vector Transformation – Reading: 2.4, 3.3–3.4
• Explain what a transformation matrix is and how it is used to solve FEM problems
• Using the finite element method calculate the following for a truss:
– Joint displacements
– Reactions
Lesson 5: Settlement; Bar Forces and Stresses – Reading: 3.5–3.6
• Analyze a truss subject to settlement using the FEM
• Calculate the force in a truss element using the finite element method
• Calculate the stress in a truss element using the finite element method
Lesson 6: Symmetry, Comparison of Bar FEM to “Exact” Solution (CECIL) – Reading: 3.8, 3.11
• Explain when symmetry can be used to simplify the analysis of a structure
• Use symmetry to analyze a structure using the FEM
• Explain how truss deflections and forces from a FEM analysis compare to the “exact” solution
using mechanics
• Explain how better accuracy for deflection and force can be found using the FEM
Lesson 7: Beam Stiffness and Assembly – Reading: 5.1–5.3
• List the assumptions made in deriving the beam element and how those assumptions affect
analysis
• Analyze a beam with point loads
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Lesson 8: Distributed Loading, Settlement – Reading: 5.4
• Explain, based on engineering principles, how equivalent nodal loads are calculated
• Calculate equivalent nodal loads for a distributed load
• Analyze a beam with a distributed load
• Analyze a beam subject to settlement
Exam #1 – Lessons 1–6 (Feb 24)
Lesson 9: Hinges and Frames – Reading: 6.1–6.2
• Explain how the stiffness matrix is modified for a “hinged” element
• Analyze a beam with a hinge
• Calculate the rotation of a beam on both sides of a hinge
• Analyze a frame using the FEM
Lesson 10: Geometric Stiffness
• Explain the P-δ effect
• Approximate P-δ effects using the geometric stiffness matrix
• Calculate the buckling force for a member using the eigenvalue
• Explain what buckling modes are and how they can be found using an eigenvector analysis
• Sketch the buckled shape of a member for an arbitrary buckling mode using the eigenvector
Lesson 11: Comparison of Beam FE to “Exact” Solution – Reading: 5.5–5.6
• Explain how beam deflections and forces from a FEM analysis compare to the “exact” solution
using beam theory
• Explain how better accuracy for deflection and force can be found using the FEM
Lesson 12: Shear Deformation
• Explain when including shear deformation in an analysis is important
• Explain how shear deformation can give misleading results in a structural analysis
• Solve a beam problem including shear deformation
Lesson 13: Introduction to “3D” Structural Analysis
• Identify factors increasing the complexity of a 3D analysis
• Explain important checks to use to verify a 3D structural model
• Use a three-dimensional model to analyze a structure
Exam #2 – Lessons 7–11 (Mar 14)
Spring Recess
Lesson 14: Dynamics of Mass/Spring/Damper System – Reading: 16.1
• Solve the dynamic equation of motion differential equation without damping
• Compare the dynamic response of a SDOF system to an equivalent static load.
UWP Distinguished Lecturer: Robert Ballard (March 28)
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Lesson 15: Single-Degree-of-Freedom Structural Systems
• Determine the stiffness of a SDOF civil engineering structure assuming the column ends are
fixed
• Determine the stiffness of a SDOF civil engineering structure assuming one column end is
pinned
• Solve for the dynamic response of SDOF civil structures
• Find natural frequency of continuous SDOF structures (Clough Chapter 8)
Lesson 16: Numeric Integration in Time, Central Difference Method – Reading: 16.3
• Explain the basic principles of numeric integration and how time discretization makes it possible
• Use the Central Difference Method to numerically analyze a dynamic structural problem
Lesson 17: Numeric Integration in Time, Newmark Method – Reading: 16.3
• Explain the difference between explicit and implicit time history analyses
• Use the Central Difference Method to numerically analyze a dynamic structural problem
Engineering Expo
Lesson 18: Multiple-Degree-of-Freedom Structural Systems
• Derive the dynamic mass and stiffness matrices for a multi-degree-of-freedom structure
• Explain how to find the natural frequencies and mode shapes of a structure
Exam #3 – Lessons 12–15 (Apr 18)
Lesson 19: Modal Analysis of Structures
• Explain the concept of “modal space”
• Use a numeric integration technique to find the seismic response of a structure
Lesson 20: Introduction to Earthquake Engineering
• Use a response spectrum to calculate the maximum modal displacement
Lesson 21: Earthquake analysis using RISA-2D
• Use Risa to find the following for a structure:
– Modal frequencies and mode shapes
– The maximum displacement and member forces using a response spectrum analysis
Exam #4 – Lessons 16–19 (May 4)
Lesson 22: Monte Carlo Simulation
• Explain how a Monte Carlo simulation can be used to estimate statistical properties of systems
• Determine statistical properties (including probability of failure) for structural components using Monte Carlo simulation
Lesson 23: Optimization
• Use the central difference method to optimize a one-dimensional problem
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• Use the steepest descent method to find the optimum of a multi-dimensional problem
• Explain how genetic algorithms find an optimum solution and draw a representation of the
solution process in the search space
• List advantages and disadvantages of a genetic algorithm for optimization problems
Dates are tentative.
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