6 FEA simulation on ABAQUS with different conditions, a report on it (2000 words) for section a. 2d stress analysis to determine a displacement vector for a node.
Budget: £20 – £250 GBP
SECTION A:
Figure 1 shows a thin rectangular plate with a through hole in the middle of the plate. The plate has a length (L) of 750 mm, a width (W) of 500 mm and thickness (t) of 2 mm, while the hole through the middle of the plate has a diameter (D) of 385 mm. A tensile load (F) of 20,000 N is applied at each end of the plate. The plate is made from a solution treated and aged nickel-based superalloy (Inconel 718). Its behaviour is elastic-plastic according to the data below.
Figure 1: Plate with a central hole
You can assume the following information: Yield strength = 1186 MPa
UTS = 1400 MPa @ engineering strain of 15% Young’s modulus, E = 200 GPa
Poisson’s ratio, υ = 0.3
I. Using a suitable FE software such as ABAQUS (or an alternative commercial package), perform a finite element analysis to determine the maximum stress developed in the plate as a result of the applied force. Where appropriate, employ suitable simplifications, assumptions or approximations for your model and ensure that boundary conditions, loading and material properties/behaviour are correctly described. A number of simulations are to be carried out by utilising different numbers of continuum (solid) type elements in the range listed below in order to investigate the effect of element size/mesh density on the output measures:
a) 30-60 b)160–300 c)600–1200 d)2500–6000 e)~9,000
Plot graphs of maximum stress in the plate versus number of elements in the model. Record the analysis time required for each of the models. Validate the predicted outputs from your model using analytical stress concentration calculations.
II. Formulate another FE analysis on the same structure but this time with an 85,000 N load applied using the ‘most appropriate’ mesh density derived from Part I. Evaluate the results accordingly and comment on any issues you may observe.
Requirements:
Write a report (not more than 2000 words excluding references, figure captions and appendices) with a brief introduction and statement of the problem/aims, a description of the modelling methodology/steps undertaken (e.g. analysis type, element type, justification for selection, simplifications, etc.), details of the data obtained (graphs showing relationship of modelled maximum stress vs. mesh density, sample displacement plots and any relevant contour plots deemed necessary) together with comments/discussion on the results and comparisons of the predicted outputs against the theoretical values (calculated). The assignment will be assessed based on a clear introduction and
CFD & FEA (04 31738), 2024/2025 - SLS
statement of the aims/objectives, structure of the report, model formulation, presentation of modelled results data, discussion of the results (you are expected to discuss any observed discrepancies between the predicted results/trends and calculated values and highlight reasons for the variations and suggest possible solutions) and conclusions arising from the simulations together with any relevant commentary/information pertaining to the problem.
This section is weighted at 70% of the assignment and the general marking criteria (incorporating expectations of English language proficiency) is detailed in the module Canvas page.
SECTION B:
The structure shown in Figure 2 was modelled using three plane strain triangular shaped elements. The loading and corresponding boundary conditions are shown together with the relevant material properties provided. The nodal coordinates are in mm.
Poisson’s ratio, ν = 0.3 Thickness, t = 100.0 mm Young’s modulus, E = 150 GPa
Figure 2: Structure modelled with plane strain elements
Requirements for Section B:
Using 2D stress analysis, determine the displacement vector of node 4 due to the loads applied on the structure and calculate the corresponding strain (ε) and stress (σ) vectors in element (3). In your solution, you will need to clearly show your working / calculations for the following components:
i) The stiffness matrix [k] for each of the 3 individual elements
ii) Formulationoftheglobalstiffnessmatrix
iii) Assembly of the system equations with the appropriate boundary conditions / unknown variables (nodal displacements, reaction forces etc.) in order that the displacements can be calculated.
iv) The corresponding [B] and [D] matrices This section is weighted at 30% of the assignment.
Figure 1 shows a thin rectangular plate with a through hole in the middle of the plate. The plate has a length (L) of 750 mm, a width (W) of 500 mm and thickness (t) of 2 mm, while the hole through the middle of the plate has a diameter (D) of 385 mm. A tensile load (F) of 20,000 N is applied at each end of the plate. The plate is made from a solution treated and aged nickel-based superalloy (Inconel 718). Its behaviour is elastic-plastic according to the data below.
Figure 1: Plate with a central hole
You can assume the following information: Yield strength = 1186 MPa
UTS = 1400 MPa @ engineering strain of 15% Young’s modulus, E = 200 GPa
Poisson’s ratio, υ = 0.3
I. Using a suitable FE software such as ABAQUS (or an alternative commercial package), perform a finite element analysis to determine the maximum stress developed in the plate as a result of the applied force. Where appropriate, employ suitable simplifications, assumptions or approximations for your model and ensure that boundary conditions, loading and material properties/behaviour are correctly described. A number of simulations are to be carried out by utilising different numbers of continuum (solid) type elements in the range listed below in order to investigate the effect of element size/mesh density on the output measures:
a) 30-60 b)160–300 c)600–1200 d)2500–6000 e)~9,000
Plot graphs of maximum stress in the plate versus number of elements in the model. Record the analysis time required for each of the models. Validate the predicted outputs from your model using analytical stress concentration calculations.
II. Formulate another FE analysis on the same structure but this time with an 85,000 N load applied using the ‘most appropriate’ mesh density derived from Part I. Evaluate the results accordingly and comment on any issues you may observe.
Requirements:
Write a report (not more than 2000 words excluding references, figure captions and appendices) with a brief introduction and statement of the problem/aims, a description of the modelling methodology/steps undertaken (e.g. analysis type, element type, justification for selection, simplifications, etc.), details of the data obtained (graphs showing relationship of modelled maximum stress vs. mesh density, sample displacement plots and any relevant contour plots deemed necessary) together with comments/discussion on the results and comparisons of the predicted outputs against the theoretical values (calculated). The assignment will be assessed based on a clear introduction and
CFD & FEA (04 31738), 2024/2025 - SLS
statement of the aims/objectives, structure of the report, model formulation, presentation of modelled results data, discussion of the results (you are expected to discuss any observed discrepancies between the predicted results/trends and calculated values and highlight reasons for the variations and suggest possible solutions) and conclusions arising from the simulations together with any relevant commentary/information pertaining to the problem.
This section is weighted at 70% of the assignment and the general marking criteria (incorporating expectations of English language proficiency) is detailed in the module Canvas page.
SECTION B:
The structure shown in Figure 2 was modelled using three plane strain triangular shaped elements. The loading and corresponding boundary conditions are shown together with the relevant material properties provided. The nodal coordinates are in mm.
Poisson’s ratio, ν = 0.3 Thickness, t = 100.0 mm Young’s modulus, E = 150 GPa
Figure 2: Structure modelled with plane strain elements
Requirements for Section B:
Using 2D stress analysis, determine the displacement vector of node 4 due to the loads applied on the structure and calculate the corresponding strain (ε) and stress (σ) vectors in element (3). In your solution, you will need to clearly show your working / calculations for the following components:
i) The stiffness matrix [k] for each of the 3 individual elements
ii) Formulationoftheglobalstiffnessmatrix
iii) Assembly of the system equations with the appropriate boundary conditions / unknown variables (nodal displacements, reaction forces etc.) in order that the displacements can be calculated.
iv) The corresponding [B] and [D] matrices This section is weighted at 30% of the assignment.
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