Tuesday, January 23, 2018

SOLIDWORKS Simulation “vs.” Analytical Solution: Which is better?

The impact of Engineering analysis, simulation, and modeling activities and the way businesses are driven worldwide are more dominant than ever before. The Indian CAE industry has been growing at a frantic pace for the past few years and this growth is reflected by the fact that thousands of young engineers are opting for careers in the analysis and simulation domains. Several multinational companies from automotive, aerospace and manufacturing sectors are setting up their development centers in India. Indian analysts are increasingly found in the global delivery teams.

For a CAD designer with no prior exposure to FEA and CFD, this is a natural question to ask. Numerical methods go back a long time and have been used to approximate solutions to problems that cannot be solved precisely. Since the 1950s, when computers became available for the heavy number-crunching of FEA and CFD, both these methods have been researched extensively; many thousands of books and research papers published; and the methodologies continuously improved and algorithms refined. FEA and CFD are sound reliable methods. Within the documents included in our SOLIDWORKS FEA and CFD Simulation products, there are validation problems that compare the numerical solution to selected problems with a closed-form analytical solution, established experimental results or solutions from other resources.

In the Engineering world, we’re often asked questions about the accuracy of FEA modeling versus reality. The answer: FEA provides the right information versus reality as long as you correctly define materials, boundary conditions and, mesh type. Next, regarding the accuracy of the software itself, we have lots of Q&A tests based on literature and recognized publications. NAFEMS, an International Association of Engineering Modelling, Analysis and Simulation Professionals, is one such example. NAFEMS has published 200 publications, covering many areas within engineering analysis and simulation. We use the NAFEMS benchmark problems in order to demonstrate the accuracy of the SOLIDWORKS Simulation software for the supported analysis such as linear statics, thermal, geometric and material nonlinearity, and linear dynamics.

Here is an example analysis:

Problem Statement:

We need to calculate the maximum deflection at the center of 40mm diameter MS round bar with a length of 4000mm. The beam is simply supported and weight consideration is self-weight due to gravity. Fig. 1 shows the model with dimensions.

Now, let us solve this example using both analytically and using SOLIDWORKS Simulation and compare the results of the same. First, let us solve using analytically.

We Know,

L = 400 cm

D = 4 cm

Material = MS

The formula for Deflection is for simply supported beam with UDL is (5/384) x (w x L^4) / (EI)

E (Modulus of Elasticity) = 2.1 x 10^6 kg /sq.cm

I = Moment of inertia of a solid circular section of diameter 4 cm

I = π d4 / 64 = 3.142 x 4^4/64 = 12.58 cm^4

w = load per meter = 9.856 kg/m = .09856 kg/cm

Deflection at Center of Beam = (5/384) x (0.09856 x 400^4) / (2.1x10^6 x 12.58) = 1.243cms.

So, to summarize analytically we are achieving deflection at the center of beam as 1.243 cm or 12.43mm

Now, let us solve the same problem in SOLIDWORKS Simulation. The modeling is also done in SOLIDWORKS. So, the integration between SOLIDWORKS CAD and SOLIDWORKS Simulation is very easy and intuitive. Fig. no 2 shows the CAD modeling of the beam.

In SOLIDWORKS Simulation, the material is applied as MS. Fig. 3 shows the material properties of the same.

Boundary Conditions are applied like simply supported fixtures at both ends and force per unit length of 96.77 N/m is applied. Beam meshing is carried out since it is made up of weldment structure. And finally, when all boundary conditions and meshing is done the simulation is carried out. And results are plotted.

Now, let plot the maximum deflection result of the same as shown in Fig.4 below. The Simulation results show the maximum deflection is 12.467 mm at center of beam.

So to conclude, let us compare analytical and SOLIDWORKS results

Again coming to the question if analytical solutions are better or SOLIDWORKS simulation results are better, we can see there is hardly 0.5-1 % of the difference in deflections. Also in virtually ALL FEA analyses, as well as closed-form mathematical solutions to engineering problems, there is a fundamental weakness: Materials are assumed to be perfect. That is, some average values for key material properties are applied seamlessly with mathematical precision throughout a given solution space. The problem is that there are no perfect materials in the world.

Thanks for reading this blog post. Engineering Technique offers affordable SOLIDWORKS Simulation services. If you need help with your engineering analysis and simulation projects, contact us and we will be glad to help.

Article Written by GAURAV HARANE – an Engineering Analysis & Simulation Specialist at Engineering Technique

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