[ Problem Description ]
[ I-Beam Cantilever ]
[ Finite Element Analyses ]
[ Input and Output Files ]
The purposes of this example are:
Displacements are computed for a cantilever beam having an I-shape cross section, and subject to two concentrated loads P = 1600 lb at the flanges of the free end in opposite direction along y axis.
Details of the I-beam geometry and externally applied loads are shown in Figure 1.
The cantilever beam has length L = 40 inches, height h = 5 inches, width w = 10 inches, and thickness t = 0.25 inches. It is constructed entirely from one material type -- Young's Modulus E = 10^7 psi and Poisson's Rate = 0.3.
Finite element analyses are computed for a variety of mesh geometrys, and compared against the results for ANSYS-5.0 shell element, and the SAP-90 shell element.
Each segment of the I-beam is modeled with five shell finite elements, four for the flanges, and 1 shell element for the I-beam web. The overall mesh geometry is controled by the parameter N in Figure 1. N = 2 means that the I-beam is modeled with only two sets of shell finite elements along its length (i.e. 10 finite elements in total).
The ANSYS-5.0 shell element is a four node flat shell element having six degrees of freedom per node in which a drilling degree of freedom based on an approach suggested by Kanok-Nukulchai [1]. The SAP-90 shell element is a quadrilateral flat shell element (six degrees of freedom per node).
Meshes N | 2 | 4 | 8 | 16 |
---|---|---|---|---|
ALADDIN's Shell Element (x 0.1) | 2.45142 | 2.50528 | 2.51482 | 2.52135 |
ANSYS-5.0 Shell Element (x 0.1) | 1.1280 | 1.8943 | 2.3378 | 2.5135 |
SAP-90 Shell Element (x 0.1) | 2.0218 | 2.3010 | 2.4562 | 2.5195 |
Meshes N | 2 | 4 | 8 | 16 |
---|---|---|---|---|
ALADDIN's Shell Element (x 0.01) | 1.38753 | 1.46572 | 1.48824 | 1.49583 |
ANSYS-5.0 Shell Element (x 0.01) | 0.6299 | 1.1112 | 1.3743 | 1.4601 |
SAP-90 Shell Element (x 0.01) | 1.0434 | 1.3116 | 1.4407 | 1.4833 |
Tables 1 and 2 summarize the transverse and horizontal displacements at Point 1 (see Figure 1) for a variety of finite element meshes. For the purposes of numerical comparison, displacements are also shown for shell elements in the ANSYS-5.0 and SAP-90 finite element packages.
Conclusions
References