ME 424 - Finite Element Analysis

Institution:

Point Park University

Subject:

Description:

The course begins with the generation of the stiffness matrix for systems of springs and cables in series or parallel connected form. Rotation of axes permits rigid element to be pin jointed to form a truss. The stiffness matrix of each member is written in terms of the global "x" and "y" axes of the truss to form the global truss stiffness matrix. Loads and supports are applied to nodes (the pin joints) to form a force vector. A vector representing the "x" and "y" displacement at the nodes is written. By Hook's law the scalar multiplication of the stiffness matrix into the displacement vector is seen to equal the force vector. After a review of bending theory the FEA method is applied to simply supported and built-in beams to form the beam stiffness matrix. Using the work equivalence concept, synthetic loads and moments are applied at the nodes to represent real distributed loads that exist between the nodes. Symmetry is used where applicable. The work on frames is combined with the work on beams to form the stiffness matrix for each element of a rigidly jointed planar structure. After globalization and the formation of a vector of applied forces and moments, the system is solved to yield a vector of "x" and "y" displacements and rotations at every node. Following a review of torsional theory the FEA method is applied to grid structures for which the loading gives rise to twisting and bending. Again a stiffness matrix for a grid element is generated. Following globalization vectors are formed for forces and moments and for displacements and rotations. Solution yields displacements and rotation at the nodes. After a review of Fourier's and Poisson's equations for heat conduction the calculus of variations is used to form conductance matrices and heat flux vectors for a variety of multi element heated or cooled objects for which nodal temperatures must be determined. Internal heat generation is accounted for. Boundary conditions include adiabatic, applied heat flux and convective heating or cooling. Prerequisite: MATH 230, MATH 310, ME 213, ME 405. Course Objectives Upon successful completion of the course, students will be able to: (1) Determine displacement of masses that are loaded and connected via springs and cables to a stationary frame. (2) Analyze two dimensional loaded, pin jointed trusses. Reactions at the supports along with displacement at the nodes are quantified. (3) Find the displacements and rotations at nodes along a beam that is subject to concentrated and distributed loads. (4) Analyze two dimensional loaded rigid jointed frames. Force and moment reactions at the supports along with displacements and rotations at nodes are found. Loading might be concentrated or distributed between nodes. (5) Analyze grid structures that are subject to bending and twisting. Force and moment reactions at the supports along with displacement and rotations at nodes are found. Loading might be concentrated or distributed between nodes. (6) Determine nodal temperatures for objects that are being heated or cooled and are at steady state. Objects might have internal heating and might be subject to applied heat flux and or convective heating or cooling at the boundaries.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.pointpark.edu

Phone Number:

(412) 391-4100

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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