ME 160 Introduction to Finite Element Method-Spring 2016 Topics for Term Projects by Teams of 2 Students Instructor: Tai-Ran Hsu, Professor, Dept. of Mechanical engineering, San Jose State University, San Jose, CA, USA Two-Tier projects for students in ME 160 class ● Tier 1 Projects: Use software (50% bonus marks for using ANSYS code. Learning and use of the ANSYS code is specified in the “course goal” in the “green sheet” of ME 160) ● Tier 2 Projects: Use computational methods learned from the course for solutions. General evaluation criteria for all projects: 1)Demonstration of learning and understanding of the FEM, 2)The degree of complexity of the signed up projects, 3)Research on missing information required for the projects, 4)Sophistication in using the FE models to demonstrate the value of this method in solving advanced analytical engineering problems that cannot be solved by available methods, 5) Demonstrate the wisdom in constructing FE models that make sense to engineering principles, and interpret FE results correctly and realistically. 6) Quality of project report (limit to 3 printed pages for the text, but with no limit on appendices) Deadline for submission project report: 4 PM, Tuesday, May 24, No late submission will be accepted.

Proposed Tier 1 Project topics Solve the Assigned Projects using ANSYS CODE (free download from: ● Description of the project (less than a page) ● Input file ● Material data file ● FE model ● Loading and boundary conditions ● Output file Show the results in graphic forms ● Interpretation of results ● Discussion on the results

Project 1.1: Determine impact load to crash the helmets (2 teams-one on each) Project 1.1(a) Cyclist’s helmet Project 1.1 (b) Football player’s helmet

Project 1.2: Comparison of stress concentration of windows of: “standard shapes”, circular and square with same open areas Project 1.3: Also use the S/N curve in the next slide to predict the fatigue life of the aluminum fuselage with 3 window configurations of: circular, square, and rectangular with round corners Treat as flat panels with normal pressure loading 2 to 3 teams Research on commercial aircraft windows and cabin pressure control, and cabin dimensions will be desirable. Treat windows on thin aluminum panels subjected to cabin pressure normal to the panel. One take-off/landing counts as one loading cycle. Radius of curvature ≈ infinity

Typical S/N curve for aluminum and steel Use maximum stress in structure as “S” to predict the “Number of cycles for “N”

Project 1.5: Determine the maximum stresses in the following perforate panels made of steel subject to 20,000 N in-plane tensile force along the horizontal coordinate: Multiple holes of the same size (size-pitch) Single hole with different diameters Single or multiple square holes (size-pitch) Project 1.4: Assess the fatigue life of (a) steel shaft (2) aluminum shaft (2 teams) (3 teams: One on each of the following): Predict the fatigue life of the steel (or aluminum) stepped shaft subject to axial tensile force of 20,000 N. You set your own dimensions on realistic solid structures:

Project 1.7: 3-D solid plate or alike (2 teams) Project 1.6: 3-D shell/nozzle assemblies (2 teams) Determine the stress fields and maximum stress in the following 3-D solid structures with additional 10 bonus marks

Tier 2 Projects Solve problems using the principle, theories and formulations of FEM learned from the course ● Description of the problem ● FE formulations used to solve the problem with references to the lecture notes or other reference sources ● Detailed computations with every major step in computation ● Input data ● Output results with graphical displays ● Verify results if possible ● Interpretation and discussion on numerical results ● Attach computer program, including MS Excel (spread sheets) if applicable

Project 2.1(a) : FE analysis of truss structure (one team) Determine the displacement components at Node 3 and the element forces for the plane truss shown in the figure. Let A = 3 in 2 and E = 30x10 6 psi for all elements. Derive the interpolation function for each element and show the element equations and the assembly of the overall stiffness equation with partitioning of the assembled overall stiffness matrix. Solution of the overall stiffness equation for nodal displacements and element stresses using MS Excel (spread sheets) ft 40 ft 5000 lb lb 30 ft

Project 2.1(b) : FE analysis of truss structure (one team) Determine the displacement components at Node 3 and the element forces for the plane truss shown in the figure. Let A = 4x10 -4 m 2 and E = 210 GPa for all elements. Derive the interpolation function for each element and show the element equations and the assembly of the overall stiffness equation with partitioning of the assembled overall stiffness matrix. Solution of the overall stiffness equation for nodal displacements and element stresses using MS Excel (spread sheets) m 3 m 60 o 5 m W = 40 kN

Project 2.2(a) : FE analysis of beam structure (one team) A redundant beam shown in the figure below is subjected to both concentrate force P and uniform distributed load w per unit length of the beam with total length L = 10 m. Use the finite element method to determine the deflections along the length of the beam. The beam has a Young’s modulus of 210 GPa, and has a rectangular cross-section with width b = 10 cm and depth h = 20 cm. The applied load includes: P = 10 kN, and w = 500 N/m. Show all FE formulations you used in this project. Project 2.1(b) : FE analysis of truss (one team) P L/2 L W N/unit length

Project 2.2(b) : FE analysis of beam structure (one team) A redundant beam shown in the figure below has an internal hinge. There is an applied weight of W = 5 kN at the hinge. Use the finite element method to determine the deflections at the hinge and point A and B. And also the bending stresses along the length of the beam. The beam has a Young’s modulus of 210 GPa and a section moment of inertia I = 2x10 -4 m 4. Show all FE formulations you used in this project. 2 m A B 1 m 1.5 m W = 5 kN

Project 2.3(a) : FE analysis of 2-D solid structures (one team) Use the finite element method to determine the 2 displacement components at each node, and 3 stress components in each element in the structure shown in the figure below. The structure is made of aluminum with Young’s modulus E = 69 GPa and Poisson’s ratio υ = 0.3. Show all FE formulations you used in this project. 10 bonus points will be allowed for using MS Excel (spread sheets) for solving the overall stiffness equation of the structure). (Unit for physical dimensions is m, and the unit for force is N) Tabulate your outputs.

Project 2.3(b) : FE analysis of 2-D solid structures (one team) Perform FE stress analysis on the 2-D solid structure as in Project 4.1(a) but with 10 times the physical dimensions and use material properties for steel with E = 210 MPa and the same Poisson’s ratio but is subject to P m = 50,000 N