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 1 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) 2 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 3 • 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. 4