### 1. Problem Description:

To analyze a simply supported pipe structure which has three operating forces acting on its top surface. There are three design options / pipe sections available to select for final manufacturing. The selection has to be made based on analytical calculations in terms of meeting performance requirements due to operating loading conditions.

### 2. Design Inputs:

Following are the additional inputs provided for this project in addition to the pictorial details provided in Figure 1 and 2 above.

– The pipe is manufactured from steel with a Young’s modulus of E = 210000MPa, a Poisson’s ratio of μ = 0.3, and yielding stress of 650 MPa.

### 3. Objectives:

- Develop appropriate FE models using 3D SOLID elements for each of the design profiles.
- Calculate and plot the peak stresses for each of the three pipes under operating loads.
- Calculate and plot the maximum deflections for each pipe.
- Calculate the safety factor for each of the pipe designs and discuss which type of pipe design to choose for manufacturing process.

### 4. Best Design Selection – Finite Element Analysis

Based on the inputs provided and the design objective set, this section of the project will be split into 3 individual analysis problems. On arrival of solution, analytical results are then consolidated for comparative study.

#### 4.1 Assumptions

– ANSYS V10.0 FEA software will be used for all the analytical calculations.

– Eight nodal 3- dimensional SOLID45 element with 3 degrees of freedom is used for FE analysis.

– As no plastic properties are provided, these problems will be treated as a pure elastic only problem.

#### 4.2 FE Model Details – 3 Designs

All the three FE models are built using SOLID 45 which is generally referred as an 8 – noded brick element. This element is very much commonly used for all 3D modeling. Mesh refinement is maintained adequate to capture the analytical results requirement. An element size of less 5mm is used. .

**PIPE 1 – Cross Section – ROUND**

As can be observed from the tabular summary and images of FE models, the mesh is adequate to capture the analytical requirements for this elastic only problem.

#### 4.3 Loads and Boundary Conditions

Material properties are provided as inputs for this project. Based on the properties, this is a standard rolled Mild Steel (normally referred as MS).

#### 4.4 Loads and Boundary Conditions

**Boundary Conditions**

Based on the construction of the pipe under operating conditions, it is simply supporting on some kind of single point of contact support (more like a bearing). These boundary conditions are translated in FEA as translational constraints as shown below. Model is constrained in vertical (X) and axial (Z) directions to simulate the simply supported boundary condition. Additionally the model is constrained in lateral (Y) direction to avoid rigid body motion in FEA.

**Force Loading**

The provided forces are applied equally divided on the line of nodes at the respective axial locations specified. Because of the mesh refinement the loads are applied on approximately about 20 nodes. The forces are applied in vertically downward direction as per input details.

#### 4.5 Analysis Results

The analytical results are discussed individually for each of the PIPE design.

**VonMises Stress (Total Stress) Plot**

In FEA, it is always difficult to determine accurately the stresses near the point of constraint location or near the point of load application. To overcome this difficulty, we apply St. Venant’s principle. According to this principle, the statically equivalent systems of forces produce the same stresses and strains within a body except in the immediate region where the loads or constraints are applied. Hence, in our current problem scenario, the stresses calculated in the center of a beam will not be affected by the way the ends are supported or the locations where the forces are applied.

Hence, to get an accurate estimate of actual stresses where the beam is loaded in the middle of the beam section, the end elements are unselected to plot the stresses. These elements are basically the ones with nodal constraints attached.

**Bending stress Plot**

Maximum Bending stress is

**111 MPa**at approximately center of the pipe axial length span.

Maximum vertical displacement is

**0.000232 m (0.232 mm)**. The displacement plot is scaled graphically 100 times for better visual understanding.

**VonMises Stress (Total Stress) Plot**

Maximum VonMises Stress is 639 MPa at the constraint location.

**VonMises Strain (Total Strain) Plot**

Maximum VonMises Strain is 0.003042 at the constraint location

**Bending stress Plot**

Maximum Bending stress is

**112 MPa**at approximately center of the pipe axial length span.

**PIPE 3 – Cross Section – SQUARE**

**Vertical Displacement Plot**

Maximum vertical displacement is 0.000252 m (0.232 mm). The displacement plot is scaled graphically 100 times for better visual understanding.

**VonMises Stress (Total Stress) Plot**

Maximum VonMises Stress is 636 MPa at the constraint location.

**VonMises Strain (Total Strain) Plot**

Maximum VonMises Strain is 0.00303 at the constraint location

**Bending stress Plot**

Maximum Bending stress is 119 MPa at approximately center of the pipe axial length span.

**PIPE 1-2-3 – Summary**

The results for all the 3 pipes are summarized in the form of a table and explained below. Basically the analytical results show that all the 3 pipes are quite similar in design and performance.

Based on relative comparison of the results, conclusion can be made on selecting the optimum pipe design for manufacturing.

#### 4.6 Design Selection

All the analytical results are summarized in a tabular form below.

Based on the tabular summary, the pipe design selected to move forward with manufacturing is the ROUND section. Below are the pointers that discuss on this conclusion.

- The vertical displacement is the least for the round section of the pipe. Hence, lower bending stress in the mid span of the pipe.
- As expected, the peak Total stress/VonMises stress is observed at the constraint location which is marginally over the yield limit at the constraint location.
- The stresses in the near vicinity of the constraint applied location & force application location cannot be considered as true stresses.
- The best location is the mid span where the tensile bending stress peaks after unselecting the end layer of elements. The stresses we see here are true stresses occurring because of the bending effect.
- As per beam bending theory, the tensile stress is seen on the outer fiber or layer of the beam which is the most critical stress than the compressive occurring on the inner layer of the beam section.
- The second section of this project sets a limit on the vertical displacement of the pipe at operating load. Hence, it is safer to select the beam with least vertical displacement which points to the round section.
- A higher vertical bending deflection induces a higher tensile stress on the outer fiber which can be critical from fatigue life point of view. A crack can initiate at a concentrated tensile stress location than a compressive stress.

The above pointers discussed support the selection of the round section for the pipe for further manufacturing. For the next section of design validation, as discussed above the round pipe section is selected.

Note: The simply supported boundary condition is simulated in FEA on a line of nodes on the outer most edges. Practically this is not possible in a bearing kind of support scenario. Typically the support is marginally on the inside to provide stable support. Hence, the analysis needs to be relooked by simulating this change for comparison with the current analysis.

### 5. Design Changes – Finite Element Analysis

Based on the inputs provided, there is a rearrangement of the components that get connected to the pipe. Hence the pipe is changing in length and the locations where the load gets applied. Below is the figure provided as input for further analysis.

#### 5.1 FE Model Details

#### 5.2 Loads and Boundary Conditions

The boundary conditions for the analysis remain the same which is simply supported. The locations for the simply supported B.C are as shown above in Fig.3. The vertical force loads reduce to half from their initial defined values for section I of the analysis. The locations for the load application points are as in Fig. 3.

#### 5.3 Analysis Results

**Vertical Displacement Plot**

Maximum vertical displacement is 0.000233 m (0.233 mm). The displacement plot is scaled graphically 100 times for better visual understanding.

**VonMises Stress (Total Stress) PlotG**

Maximum VonMises Stress is 1500 MPa at the constraint location. As mentioned earlier, this stress is not the true stress as it is at the constraint location. VonMises Strain (Total Strain) Plot

Maximum VonMises Strain is 0.007128 at the constraint location

**Bending stress Plot**

Maximum Bending stress is 175 MPa at approximately center of the pipe axial length span.

#### 5.4 Results Discussion & Conclusion

The main constraint based on customer’s requirement is the vertical displacement. Following are the few pointers which are used to conclude on the analysis results.

– The vertical displacement from the new analysis is less than 0.3 mm. Hence, it meets the major criteria set up by the client.

– The stresses are slightly exceeding the yield limit. The model needs to be looked more closely in simulating the boundary conditions. Also minor changes in the cross section of the pipe (change in stiffness) can help in reducing the stresses.

– Bending stress increased as compared to the Section – I design stresses. Hence, as mentioned in the above pointer, making minute changes in the cross section of the (changing diameter of the pipe hole) pipe can effectively change the stiffness of the pipe and in turn the stresses.

To conclude the design meets the deflection criteria and can be released for manufacturing after looking at making small changes to the pipe and also simulating more accurately the boundary conditions ( modeling the supports and using contact elements at the interface ). By using contact elements, the boundary conditions will be more realistic and result in true stresses which are closer to reality.

### 6. Stress Analysis using FEM – Discussion

This section is to discuss FEA in general as how effectively this has been made use to make decisions on designs in any field. The following points will be discussed in this section:

2. Advantages and disadvantages of FEA.

3. Possible mistakes that can occur in the process of FEA usage.

4. How to assure that FEA results are right and make sense.

**FEA applicability in the current competitive world**

Finite element analysis is nothing but a group of software tools which use Finite Element Method principles to obtain a solution for any product design validation. The Finite Element method should be understood as a method for finding an approximate solution for a simplified model (Barna Szabo, 1991, P.4). The finite word is used because the component made of infinite parameters is discretized into finite number of mathematical parameters to obtain a approximate solution. Because of this manner of simplified solving any design problem, Finite element analysis has been extensively used in all fields of product development and validation. We can see the usage of FEA starting from a small fastener to a huge airplane to prosthetic leg. Hence, the applicability of FEA (Finite element analysis) is vast. Stress analysis is one of the important and major types of evaluation which uses Finite Element Method. Traditionally FEM was developed for stress / structural analysis itself. As technologies developed, different domains started applying FEM for developing codes to analyze design problems (example: thermal, fluid, electro-magnetic, etc.).

**Advantages and disadvantages of FEA**

**Finite Element Analysis – Advantages**

– Any design process is iterative involving designing and validating. FEA is very useful in all such situations where in validation part can be automated which reduce the cycle time. Without FEA, validation by building prototypes is not highly practical because of high cycle time and involves lot of time and financial investment.

– Finite element analysis software tools are very user friendly and do most of the mathematical calculations involved. For example if the proper material properties are provided it can calculate the fatigue life if exposed to particular load conditions.

– Using reverse engineering techniques any existing old designs can be revalidated using FEA to ensure the design is good enough for the intended life. In this manner any old design from the early period when computers were not yet invented, FEA can validate the design and build the confidence of engineers into the design.

**Finite Element Analysis – Disadvantages**

– FEA tools are just another software code with a user interface front end. It is the engineer’s responsibility to ensure the correctness of the calculations.

– The results or the outputs from FEA are always as good as the inputs. For example a bad / wrong material property will result in some output which may not be necessarily true and correct.

– FEA cannot be implemented in each and every situation. In cases where the design involves few iterations and the design is simple enough, only hand calculations or a simple prototype would serve the purpose.

– End user of the FEA software needs to have thorough knowledge and experience to judge and make something out of the outputs. Everyone cannot just start using FEA. It needs knowledge and training in the domain the person is trying to work.

– Correctness of the finite element analysis outputs depend highly on the manner the code is written and how correctly it is written.

– Initial investment in terms of training, software and hardware infrastructure is huge. Any individual or firm should have proper justification to make this investment.

(Finite element analysis David Roylance MIT February 2001)

**Possible mistakes that can occur during FEA process**

All FEA software packages are essentially computer language codes. The coding part brings in the complexity into the package. So, essentially there are huge chances of mistakes occurring. Following are few frequent ways the FEA validation process can go wrong.

– FEA design validation outputs are as good as inputs. Being fully aware of the system units is one very important thing. If the input parameters are not consistent in units, then outputs will be wrong.

– Usage of improper material properties will result in wrong results.

– Being unaware of the software and hardware requirements can change the whole design validation process resulting in delays.

– Not having thorough knowledge of the software limitations and the manner it provides the outputs etc… can result in wrong design decisions.

– Without understanding the physics of the problem and relying too much on the software can result in wrong loading conditions, boundary conditions and hence bad designs.

**How to assure that FEA results are right and make sense**

When reviewing the FEA results or outputs keeping in mind the following pointers or steps will help to increase the confidence level in the correctness of the results. Basically, FEA results or outputs are just a bunch of numbers coded to specific colors for ease of understanding pictorially. But, it is the design engineer’s responsibility to ensure everything is correct. Following few pointers can be reviewed by the engineer before signing off on the correctness of the results.

– The units so that they are consistent between model, material properties, loads and results.

– Loads and boundary conditions are simulated as closely as possible to the physics of the problem.

– The analysis has converged with a tight enough tolerance as per standard practice or FEA package recommendations.

– Finite Element Model / mesh is optimum enough to ensure the region of interest is captured well to simulate the physics of the problem accurately.

– Quick hand calculations using text book formulae by simplifying the model to cross check if FEA predicts the similar results.

– Checking if the FEA results are similar in pattern and behavior as any past design models.

Once the above pointers are checked and reviewed for correctness, then the FEA results can be relied upon for further design study process.