SOLIDWORKS Simulation: Nonuniform Force and Pressure Loading in Spherical Coordinate Systems

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In previous posts “SOLIDWORKS Simulation – Nonuniform Force and Pressure Loading“, and “SOLIDWORKS Simulation: Nonuniform Force and Pressure Loading in Cylindrical Coordinate Systems” I showed how to apply boundary conditions based on Cartesian and cylindrical coordinate systems (CS). I varied the water pressure with depth on the walls of an aquarium in the first post. In the second, I varied the wind load on a horizontal storage tank. Let’s now look at nonuniform pressure loading using the third option, a spherical CS. We’ll examine the effect of wind loading on the dome structure shown below.

Figure 1: Dome Structure: full (left), cutaway (right)

Figure 2: Direction of Side Wind

Within a SOLIDWORKS Simulation static study, we define materials for the cover and structural frame and add supports to attach the dome to the ground. For thin wall components like the cover, shell meshing is appropriate; for the frame, beam meshing is best.

Figure 3: Simulation Static Study Initial Setup

Assume a maximum pressure value of 0.2 psi generated from the wind impacting the structure. Note that Civil Engineering references can help estimate pressure fields from wind loading. The pressure varies as the air moves over and around the dome, so we can activate the nonuniform pressure distribution. This feature is available within both the force and pressure load property managers. The variation can be applied relative to a Cartesian, cylindrical or spherical CS.

Figure 4: Available Coordinate System Types for Nonuniform Loading

For this side wind load, the air pressure is highest where the wind impacts it directly and is forced to go around the spherical shape. As it moves around the dome with increasing velocity, the air pressure drops to zero, or possibly slightly below atmospheric pressure depending on the wind velocity. For this analysis, we’ll assume that it goes to zero and use the spherical CS option in the pressure boundary condition definition to represent the pressure distribution with an assumed sine function. To facilitate this relationship in Simulation, a SOLIDWORKS reference CS is first created at the dome center so that the radial “r”, longitudinal “t” and latitudinal “p” directions align with the X, Y and Z axes, respectively. The resulting “Dome Center CS” is shown below.

Figure 5: SOLIDWORKS Reference Coordinate System at Center of Dome

We start a pressure load boundary condition, select the “Use Reference Geometry” option with the right plane used for direction, as shown below, and select the windward face of the dome cover for the pressure application surface. Select “psi” as the Pressure Value unit. In the Pressure Value field, enter 0.2 psi, which is the maximum value that occurs. Check the Nonuniform Distribution box and use the “Dome Center CS” in the reference CS field. Select “radians” as the angular unit, then pick the Edit Equation button and enter the function “sin(“t”) – sin(“p”)” for the equation.

Figure 6: Pressure Load Property Manager (before adding equation for pressure distribution)

Figure 7: Nonuniform Pressure Spherical Equation Editor

The constant value in the Pressure Value field is multiplied by the equation, resulting in the variation of pressure over the dome as shown below. The boundary condition icons qualitatively confirm that our setup is correct with maximum pressure applied at the center and decreasing to zero as the flow direction becomes tangent to the dome surface.

Figure 8: Pressure Variation on the Dome Wall

After solving the analysis, we find that the maximum deflection of the cover is 0.04 inches, the von Mises equivalent stress in the frame is around 1,400 psi and the frame deflection is 0.01 inches.

Figure 9: Deformation of Dome Cover

Figure 10: von Mises Equivalent Stress Distribution in Frame

Figure 11: Resultant Displacement in Frame

This wraps up our look at nonuniform pressure loading for all three coordinate system types. I hope this helps increase your understanding of applying loading conditions in SOLIDWORKS Simulation. Thanks for taking a look!

Kurt Kurtin
Manager, Simulation, and Electrical Products
Computer Aided Technology, LLC