Fundamentals of Modern Manufacturing, Binder Ready Version: Materials, Processes, and Systems
6th Edition
ISBN: 9781119128694
Author: Mikell P. Groover
Publisher: WILEY
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Chapter 14, Problem 1RQ
To determine
The principal polymers used in fiber- reinforced polymers.
Expert Solution & Answer
Explanation of Solution
FRPs are otherwise called Fiber-reinforced plastic. It is a mixture of polymer and glass fibers. They are not only mixed with glass fibers, but also with paper, wood or carbon fibers. The polymers that are mainly used are epoxies, vinyl ester, phenol formaldehydes and all.
FRP are examples for composite materials. They are made by mixing entirely different natured materials in order to get improved results regarding its strength, and quality.
Epoxies are group of polymers containing the epoxide group. Unsaturated polymers are polymers that contain double bonds and triple bonds between the atoms. Epoxy resins are the major constituents in the preparation of adhesives, plastics, paints and also some glass coatings.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 14 Solutions
Fundamentals of Modern Manufacturing, Binder Ready Version: Materials, Processes, and Systems
Ch. 14 - Prob. 1RQCh. 14 - Prob. 2RQCh. 14 - Prob. 3RQCh. 14 - Prob. 4RQCh. 14 - Prob. 5RQCh. 14 - Prob. 6RQCh. 14 - 14.7 Why are laminated FRP products made by the...Ch. 14 - Prob. 8RQCh. 14 - Prob. 9RQCh. 14 - Prob. 10RQ
Ch. 14 - Prob. 11RQCh. 14 - Prob. 12RQCh. 14 - Prob. 13RQCh. 14 - Prob. 14RQCh. 14 - 14.15 How does pulforming differ from pultrusion?
Ch. 14 - Prob. 16RQCh. 14 - Prob. 17RQCh. 14 - Prob. 18RQCh. 14 - 14.19 Name the four basic categories of processes...Ch. 14 - Prob. 20RQCh. 14 - Prob. 21RQCh. 14 - Prob. 22RQCh. 14 - Prob. 23RQ
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