Deflection Study on Beams with COMSOL Finite Element Analysis
Gao, Jie (2020)
Gao, Jie
2020
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:amk-202005149097
https://urn.fi/URN:NBN:fi:amk-202005149097
Tiivistelmä
The main orientation of the thesis is to present and compare the discrepancy between two delegative beam theories which are prevalently applied in both civil engineering and structural analysis. The objectives of the thesis are eventually achieved via Comsol computation and by observing the stress distribution along the beam elements and deformation after importing either a force or moment to the domain. Beams with various thickness and different transverse sections such as square, rectangular and I-beam are input for differentiation.
There are 24 simulation occasions presented in total. By using beam modulus for analysis, to a large degree, results are acquired more accurate when compared with the mathematical calculations on both critical values of stress and displacement than ones from solid mechanics. In conclusion, when objects of a still length are under study for both bending and torsion cases, if the thickness of beams increases, Timoshenko Theory can result more precise on deformation (larger displacement at free end) than Euler-Bernoulli Theory. For instance, the maximum normal stress of square beam due to surface load is 10,5 MPa with displacement of 0,399 mm whereas, both Euler-Bernoulli and Timoshenko formulation manage to obtain the stress value of 10,5 MPa. However, beams under Timoshenko Theory captures a larger displacement with value of 0,345 mm rather than 0,339 mm.
Another parameter which may affect the final findings is the length of the beam. Referring to the concept mentioned in literature review, length-to-thickness ratio somehow will influence precision of results. Hereby, how precise the results are will depend on the length-to-thickness ratio rather than only relying on thickness of the beam.
There are 24 simulation occasions presented in total. By using beam modulus for analysis, to a large degree, results are acquired more accurate when compared with the mathematical calculations on both critical values of stress and displacement than ones from solid mechanics. In conclusion, when objects of a still length are under study for both bending and torsion cases, if the thickness of beams increases, Timoshenko Theory can result more precise on deformation (larger displacement at free end) than Euler-Bernoulli Theory. For instance, the maximum normal stress of square beam due to surface load is 10,5 MPa with displacement of 0,399 mm whereas, both Euler-Bernoulli and Timoshenko formulation manage to obtain the stress value of 10,5 MPa. However, beams under Timoshenko Theory captures a larger displacement with value of 0,345 mm rather than 0,339 mm.
Another parameter which may affect the final findings is the length of the beam. Referring to the concept mentioned in literature review, length-to-thickness ratio somehow will influence precision of results. Hereby, how precise the results are will depend on the length-to-thickness ratio rather than only relying on thickness of the beam.