EIGENVALUE ANALYSIS OF A SHELL-SOLID BEAM Application Note

Transcription

1 EIGENVALUE ANALYSIS OF A SHELL-SOLID BEAM Application Note

2 Objectives: Create an Akselos model using a Shell-Solid combination. Define materials, loads and boundary conditions. Prepare the model for modal analysis. Visualize analysis results. Model Description: The model below is a finite element representation of a Solid-Shell model. Each component is 1 meter long. We will arrange 4 of them to create a 4-meter beam system. Dimensions of this beam are shown in Figure 1a, Figure 1b and Table 1. Fig. 1a: Component Schematic Fig. 1b: Component Schematic 1

3 Elastic Modulus 200 GPa Poisson Ratio 0.30 Density 7850 kg/m 3 Shell thickness Table 1: Model Properties 10 mm Suggested Exercise Steps Create the model in Akselos Modeler. (Refer to the Component Editor tutorials in the Akselos User Manuals to learn how to create components.) Define materials. Apply boundary conditions and loads. Upload model to Akselos Dashboard and run the component training process. Solve model with RB-FEA solver type. Review the results and compare with theories, full solid model and full shell model. Hand Calculations Based on Roark's Formula for Stress and Strain (7th edition), Equation 3b from Table 16.1, Chapter 16, page 765, we have: K f n = n EIg 2π ωl 4 Where: K n is a constant where n refers to the mode of vibration; ω is load per unit length including beam weight (Newtons/metre) ω = ρ ga Hence: f n = 2π K n ( ) = K n Based on Roark, we have values of K n, then we can calculate f n. Mode K n f n (Hz)

4 Create Model Create a new collection Specify the Physics as elasticity_eigen Create the component. There are 3 subdomains, which are shown in Figure 2 below. Note that, Subdomain 2, which is highlighted with yellow, is the part of the solid component that the Shell part breaks through. Figure 2: 3 subdomains of the component Figure 3: Beam system after arranged Set up Boundary Conditions. Clamp all directions at the solid side. 3

5 Figure 4: Boundary Conditions Upload the model to Akselos Dashboard and run the component training process. Solve model with the RB-FEA solver. Review the results. Results Figure 5: mode 1, Frequency 1 = 6.53 Hz 4

6 Figure 6: mod 2, Frequency 3 = 40.6 Hz Figure 7: mode 3,Frequency 5 = Hz Table 2 below represents the comparison of the results with theoretical results for a full solid model and a full shell model. Mode Theory Shell-Solid Full Solid Full Shell Table 2: Eigenvalue Frequency Results (unit: Hertz) 5

7 About Akselos Akselos is a digital technology company headquartered in Switzerland, with operations in Europe, the USA and South East Asia. The company has created the world s most advanced engineering modeling, and fastest simulation technology, to protect the world s critical infrastructure today and tomorrow. The technology has the power to revolutionize how we build and manage our critical infrastructure, and pushes the boundaries of what modern engineering and data analytics can achieve. Developed by some of the world s best minds, the MITlicensed technology builds something far beyond the capability of a conventional digital twin a digital guardian that allows operators to not only monitor an asset s condition in real time, but helps them to see the future. North America Europe/Middle East/Africa Asia-Pacific AKSELOS, Inc 210 Broadway, #201 Cambridge, MA 02139, USA AKSELOS S.A. EPFL Innovation Park, Building D 1015 Lausanne, Switzerland AKSELOS Vietnam 125/167 Dinh Tien Hoang street, Binh Thanh Dist. Ho Chi Minh city, Vietnam