ME5013 Failure Assessment And Finite Element Analysis Assessment Answer

Use appropriate CAD/CAE tools for the design to create an effective mechanical model and system and simulation and analysis.

Description

In this section, a simply supported, straight beam 10000mm long, 2000mm width, 500mm thick made off structural steel (modulus of elasticity E=210GPa, Poisson’s ratio ν=0.3) will be examined. The beam will be subject to a three-point bending test, the external load is considered as a vertical load of 7000N. A stress constraint of 140MPa and a deflection constraint of L/1000, L is the span of the beam, are also imposed.

Aims

The aim of this assignment is for the students to become familiar with the application of the Finite Element Method in analysing a slender structural member, as well as to understand how various design parameters and constraints affect the accuracy of the solution and the computational cost.

Objectives

The objectives of this assignment are the following:

1. To understand basic terms regarding the Finite Element Method (FEM).
2. To be able to model and analyse a structural member using beam elements.
3. To be able to verify numerical results against analytical solutions (for the case of a slender beam).
4. To be able to get mesh independent results when using beam elements.
5. To be able to minimize the weight of the beam under given stress and displacement constraints.

Section A – Theoretical questions (15%)

1. What is a ‘three-point-bending’?
2. What information can be retrieved from a ‘three-point-bending’ test?
3. What is ‘Finite Element Analysis (FEA) of a structure’?
4. In FEA, what is ‘pre-processing’ of a model?
5. In FEA, what is ‘post-processing’ of a model?
6. In FEA, what is a ‘Degree of Freedom’?
7. In FEA, what is a ‘Reaction Force’?
8. In FEA, what is a beam element?
9. What is the stiffness matrix of a beam element in 2D?
10. What is the physical interpretation of each one of the entries in the stiffness matrix of a beam element in 2D?

Section B – Analytical calculation of the beam (10%)

For the shape selected in Description above, and draw a sketch showing the beam under a three-point bending test (use the given point load). Supports and external loads must be clearly shown and justified. Sketch the Free Body Diagram of the beam and calculate analytically (hand calculations) the maximum shearing force, the maximum

bending moment, the maximum deflection and the maximum normal stress due to bending. The hand calculations must be clear and complete. Also, fully define all the necessary information for these calculations and justify your selections. Initially, ignore the self-weight and then repeat the calculations including the self-weight.

Section C – Finite Element Analysis of the beam (by hand) (20%)

For the purposes of the current section, model the entire beam as an assembly of two- beam elements and, after carrying all calculations by hand, get a solution for the vertical deflection. More particularly, for each one of the two elements, write the stiffness matrix and, based on that information, update/form the global stiffness matrix of the structure. In the sequel, apply proper boundary conditions and solve the so formed system of equations. For this very last step (solution of the system of equations), any software (e.g. MatLab, MS Excel, etc.) may be used. After getting a solution for the nodal displacements, estimate the maximum deflection, the maximum bending moment, the maximum shear force and the maximum normal stress due to bending.

Section D – Finite Element Analysis of the beam (20%)

Repeat Section C, this time using Siemens NX10. In more details, develop a CAD model for a beam under a three-point bending test. Fully define all the necessary properties,

e.g. cross-section, material, supports, external loads, etc. Fully justify the selection of boundary conditions. Apply the techniques used in Section B for six different meshes of your choice (justify the selection). Plot the maximum deflection versus the corresponding degrees of freedom (use the degrees of freedom as an indicator of the computational cost). Determine for which number of elements the results are mesh independent. Initially, ignore the self-weight and then repeat the analysis including the self-weight.

Section E – Comparison between analytical and numerical results (20%)

• Compare the results from Sections B and C and calculate the % error between the analytical solutions and the numerical solutions. Comment on any discrepancies and justify your answer.
• Compare the results from Sections B and D.

Section F – Optimization (10%)

Using FEA only, determine from catalogues the beam profile that complies with the imposed constraints and corresponds to a beam of minimum weight. To this end, several trial-and-error attempts may be required. Illustrate them in the following plots:

• Maximum stress vs the second moment of area
• Maximum deflection vs the second moment of area
• Maximum stress vs cross-sectional area
• Maximum deflection vs cross-sectional area Comment on the plots.

Section G – Conclusions (5%)

Discuss whether the aims and objectives stated in the beginning have been achieved. Fully justify your answer.

Report Structure

The individual report must include all the above-mentioned sections A, B, C, D, E, F, G with the specifically requested information.

Be careful to include in section D

• Schematic Diagram

This should include two subsections:

1. A brief description of the system with details of the main function of each component.
2. Details about the function of the main components and the forces flow as diagrams and/or flowchart. Details on the assumption used to model the part selected are required. The connections between the selected part and the rest of the system should be provided to support the assumption.

• Preliminary Analysis

This should include two subsections:

1. Describe any hand calculation used to derive the forces acting on the subsystem. Details on the assumptions for the validity of the hand calculation should also be included. The hand calculation should show reaction force values and the detailed workout.
2. Details on the material properties and the implementation of it in the FEA is required. You should also discuss the effect on the degree of approximation of your assumption.
3. The simplifications used for the geometry based on symmetry and features not significant for the analysis should be discussed and presented using the minimum number of images required.
4. The preliminary Finite Element Model (FEM) implemented used beam or plane elements to provide a rough estimation of the structural response.

• Simulation set up and Mesh Sensitivity

This should include:

1. Details of Finite Element Modelling developed using the full model describing the element used as well as the process adopted to check the quality of the mesh. Details of the material model must be provided.
2. Mesh sensitivity should be reported and discussed.
3. The definition of the Boundary Conditions used to constrain the model, the loading conditions considered as well as any rigid constraints should be discussed with diagrams and images.
4. The details of the setting used in the software to solve the particular problem should be reported as a print screen of the actual software and discussed to provide enough details of a clear understanding.