Nonlinear dynamic analysis of a blast wall stiffener
1. Introduction
Blast or explosion response studies are often necessary to ensure that critical structures or equipment can survive and/or limit the escalation of an explosion event. An example of this, in an offshore environment, is a blast wall that divides process and utility areas. The blast wall should be designed to resist the explosion overpressure, but also prevent escalation of the hazard by providing a physical barrier to any subsequent jet or pool fires.
The explosion overpressure magnitude and spatial variation is highly variable since it depends on factors such as the fuel source, inventory size, leak duration and ignition location. As a result, explosion overpressure calculations should provide a range of the most probable explosion scenarios. The structural assessment proceeds through a number of stages as follows:
1. Pre-screening – selection of a representative range of scenarios taking into consideration the explosion overpressure, duration and spatial distribution.
2. Screening – simplified analysis (using Biggs SDOF method or simple Abaqus beam model) to calculate the capacity of the main load carrying components.
3. Refined analysis to capture three dimensional effects, detailed response of the boundary supports, the capacity of welded or bolted connections, local buckling of stiffeners etc.
This assignment is concerned with the screening stage and the main aim is to compare results from the Biggs SDOF method with a simple Abaqus beam model. Brief information on the Biggs SDOF method is included in the appendix.
This assignment contributes 25% of the final grade. The deadline is noon 20th April 2020 (BST).
2. Problem description
The geometry, boundary conditions and loading of the simple beam model are shown in Figure 1. Note the cross-section is orientated to provide maximum bending stiffness under the applied load.
Figure 1. Beam geometry, boundary conditions and loading.
EG55M1/EG5596 FEA
2
The beam is made from a steel material with Young’s modulus 210 GPa, Poission’s ratio 0.3 and density 7850 kg/m3. There are two nonlinear material models considered for the beam material, an elastic perfectly-plastic model, with yield stress 345 MPa, and a strain hardening model (Table 1).
Table 1. Stress-strain data for strain hardening material.
Engineering Strain Engineering Stress (MPa) 0.0016 345 0.0040 355 0.02 358 0.15 470
The blast loading is applied as a uniformly distributed load on the beam (Figure 1) and the dynamic loading profile is idealised as a triangular pulse (Figure 2), where td = 10 ms and Pmax is defined in the tasks below. Assume the pressure is applied over a 1 m width.
Figure 2. Dynamic loading profile.
3. Assignment tasks
Complete the four tasks detailed below using the information in this handout and other relevant sources. The model, results and analysis for each task should be detailed in a single report, which should be submitted through MyAberdeen (you do not need to submit your Abaqus files).
Task 1
Use Abaqus to create a nonlinear dynamic FE model of the blast wall stiffener beam (as detailed in Section 2). Modelling aspects to consider are: • element type and mesh density, • analysis procedure and options.
Describe the model in your report and justify your choices for the above aspects. Also, you should convert the engineering stress and strain data in Table 1 into true stress and strain, as this is the data required by Abaqus for the strain hardening model.
EG55M1/EG5596 FEA
3
Task 2
Run the analysis with two different load magnitudes (see Figure 2): Pmax = 1.05 bar and Pmax = 2.10 bar. Also, run the model with both material models (this gives four scenarios in total).
Obtain results from the FEA for beam central displacement and total reaction force (in the direction of the loading). Compare these results with those obtained by the SDOF Biggs model (see separate Excel file called “Results-Biggs_data.xlsx”) and comment on any differences.
Hints – The results for Pmax = 1.05 bar with elastic perfectly plastic model should closely match the Biggs data for 1.05 bar, up to about 25 ms. Try plotting various energy values to help investigate any differences in the results.
Task 3
The boundary conditions in Figure 1 show a slider constraint at the top. This eliminates any resistance through membrane action. To investigate this effect, repeat task 2 with pinned-pinned boundary conditions and comment on the results.
Task 4
For rapid events such as this, strain rate effects can be significant. To investigate this, add strain rate effects to the strain hardening material model and run the analysis with Pmax = 2.10 bar and original boundary conditions (as in task 2).
In Abaqus, use the power law model to represent the strain rate (i.e. Cowper-Symonds strain rate) with the following data, D = 40.4s-1, n = 5 (Hint – check Abaqus documentation to find out how to apply this in CAE). Compare results with those without strain rate effects (i.e. using results already obtained in task 2) and comment on any differences.
Weighting
The report will be marked with the following weightings applied:
Task 1 25% Task 2 25% Task 3 20% Task 4 20% Presentation and style 10%
EG55M1/EG5596 FEA
4
Appendix: Biggs SDOF model
The Single Degree of Freedom (SDOF) Biggs model assumes an undamped system with elasto-plastic material model (see Section 2.7 and 2.8 of Biggs, 1964). The nonlinear dynamic model is then solved either analytically, or numerically.
The Biggs model suffers from the following shortcomings:
1. It does not incorporate the effects of support stiffness.
2. It does not account for the different moment capacities at the supports.
3. It ignores the catenary action from axial restraint, which has a significant influence on the member response at large displacement.
4. It ignores the influence of material strain-rate sensitivity and strain-hardening.
5. It does not account for the beam/column effect in load-bearing members that sustain significant compressive axial forces.
Biggs, J.M., (1964). Introduction to Structural Dynamics. McGraw-Hill, New York.
