1 PROJECT XXXXXXXXXXENGIN 211L Engineering Math PART 1: Finite Element Analysis Submission: • Submit Part 1 via Blackboard as a single pdf or Word document, with the exception of MATLAB code...

The assignments in general are below. They are mainly about using MatLab. Should you accept them, we can discuss it further. 3 Assignments of the same class in total. Thank you!


1 PROJECT 4 ENGIN 211L Engineering Math PART 1: Finite Element Analysis Submission: • Submit Part 1 via Blackboard as a single pdf or Word document, with the exception of MATLAB code (m-files). If some portion of your project is handwritten, submit it as a black and white scan (not a color scan). Scans must be high contrast with no shadows. Use a dark pen or pencil on unlined paper for best scanning results. Several free apps are available to turn your phone into a scanner that generates PDFs. • Optional: Include any MATLAB code you used to do this project either as a separate m-file or pasted into your Project pdf/Word document. Six springs with different spring constants ki and unstretched lengths Li are attached to each other in series. The endpoint B is then displaced such that the distance between points A and B is L = 1.5 m. The unstretched lengths of the 6 springs (in meters) are the following: Spring 1 Spring 2 Spring 3 Spring 4 Spring 5 Spring 6 Unstretched length Li (m) 0.18 0.22 0.26 0.19 0.15 0.30 Task: Determine the internal deformation of this material made of springs by following Steps (a) – (e) below. That means, find the positions x1, x2, x3, x4, x5 of the endpoints of the springs. Points: Total 35 points in Part 1. The total Project 4 score (100 points possible) will be the sum of Part 1 (35 points) and Part 2 (65 points). Your springs constants are provided in the table on Page 2. 2 Constitutive Law: The force Fi in each spring is given by Fi = ki ∆xi where ki is the spring constant and ∆xi is the extension of the spring beyond its unstretched length Li. (a) Write the constitutive law for each Spring #1 – 6. (6 points) Interfacial Condition: At the connection points (nodes) between two springs, the forces Fi and Fn of the two springs must balance each other: Fi = Fn (b) Write the interfacial condition (force balance) at every node in the system in the form Fi = Fn to show which spring forces are equal. Do not plug in the constitutive laws yet. There should be no k’s or L’s, just F’s. (5 points) (c) Combine the equations from Steps (a) and (b) into a set of dependent linear algebraic equations. Using algebra, move all the unknown xi’s in each equation to the left side and everything else that is known (Li’s, ki’s) to the right side of the equals sign. Use your assigned spring stiffnesses {ki}. (10 points) (d) Convert your results from Step (c) into a matrix equation Ax = b. Clearly define the coefficient matrix A, the right-hand side b, and the vector x containing in the unknown positions xi. Use your assigned spring stiffnesses {ki}. (9 points) (e) Solve the system using MATLAB to find the unknown positions x1, x2, x3, x4, x5 of the endpoints of the springs. (5 points) Last Name First Name k1 (kN/m) k2 (kN/m) k3 (kN/m) k4 (kN/m) k5 (kN/m) k6 (kN/m) Abukar Abdirahman 6.5 9.8 17 11.8 8.5 19.7 Aldakheel Saud 9 8.2 17.1 10.4 11.5 15.5 Asha Anas 8.5 10 17.2 12.8 11.3 19.4 Baraty Lily 7.2 10.3 13.4 11.7 9.4 18.5 Cuevas Elyanna 6.9 7.6 13 11.2 8.6 20.5 Gabardi Rudy 7 9.7 14.2 10.2 11.4 16.4 Li Kevin 6.8 10 15.8 13.8 8.5 15.3 Lico Yanni 9.2 7.7 16.5 10.4 11 17.3 Louissaint Aser 7.9 9.7 14.3 10.5 8.9 19.7 Martinez Lenny 9.2 10 12.8 13 10.6 19.9 Nguyen Austin 8.8 9 12.8 13.3 11 16.7 Onwuchekwa Chukwunodebem 8 9.9 17.1 12.4 11 19.7 Shea Michael 7.1 9.6 16.2 10.2 8.6 20 Sweeney Stedmon 7 8.1 16.6 12.1 9.3 19.3 Wei Jinfeng 8.8 7.8 14.8 13.7 8.5 19 Wei Pengcheng 9.1 10.2 16 11.5 9.7 20.5 Wu Zhiyong 8.4 10.1 17.3 10.5 9.1 15