Abstract
Finite element method (FEM) is a general numerical method to solve differential equations. Applied Element Method (AEM) is also a numerical method, but limited for structural analysis. Instead of node-to-node connection in FEM, applied elements are connected by springs. Stiffness matrix is for a pair of spring rather than for an element. A pair of spring consists of two springs to simulate normal stress (normal spring) and shear stress (shear spring) for a two-dimensional (2D) element. A comparison of AEM and FEM in terms of convergence and processing time is done in this paper. For this, 2D linear and non-linear analysis of structures is carried out. Although the processing time depends upon the features of the computer, the comparison of the results of AEM and FEM on the same system is done. In general, the analysis by AEM takes less time when compared to FEM. This is attributed to the lesser number of degrees of freedom per element in AEM. This reduces the memory requirement in AEM compared to FEM, for same meshing. In the case of linear analysis, AEM is found to be superior when compared to FEM with respect to accuracy. The results from both AEM and FEM converged at almost the same rate. Incremental method of non-linear analysis was attempted. To incorporate material non-linearity in AEM, the stiffness of the springs is varied according to its strain. Both AEM and FEM predicted similar load–deflection curve.
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Abbreviations
- α :
-
Angle of inclination of the line connecting the centre of the element and spring from the x-direction
- ε :
-
Strain
- σ :
-
Stress
- a :
-
Centre–centre distance between elements
- b :
-
Width of beam
- d :
-
Depth of beam
- l :
-
Length of beam
- n l :
-
Number of elements along the length direction
- n d :
-
Number of elements along the depth direction
- t :
-
Thickness of the element
- A :
-
Area of cross section
- E :
-
Young’s modulus of the material
- F :
-
Force vector
- G :
-
Shear modulus of the material
- I :
-
Moment of Inertia
- K :
-
Stiffness matrix
- K n :
-
Stiffness of normal spring
- K s :
-
Stiffness of shear spring
- L :
-
Distance of the spring from the centre of the element
- U :
-
Displacement vector
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Christy, D.L., Madhavan Pillai, T.M., Nagarajan, P. (2020). A Comparison of Applied Element Method and Finite Element Method for Elastostatic Problems. In: Prakash, R., Suresh Kumar, R., Nagesha, A., Sasikala, G., Bhaduri, A. (eds) Structural Integrity Assessment. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-8767-8_26
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DOI: https://doi.org/10.1007/978-981-13-8767-8_26
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