00:29 Important questions about Finite Element Analysis
21:08 Evolution of Finite Element Analysis
There is a difference between measuring deformation and analyzing stress
For example, 1D element could be used and deformation could be measured in multiple directions
- Number of nodes =
- Stiffness matrix โ
45:14 Finite Element Analysis Steps
Extra reading
How is the ๐๐จ๐ง๐๐๐ฉ๐ญ ๐จ๐ ๐๐๐ ๐ซ๐๐๐ฌ ๐จ๐ ๐ ๐ซ๐๐๐๐จ๐ฆ (๐๐๐ ) defined in Finite Element Analysis (๐ ๐๐)
๐ฏ How is the ๐๐จ๐ง๐๐๐ฉ๐ญ ๐จ๐ ๐๐๐ ๐ซ๐๐๐ฌ ๐จ๐ ๐ ๐ซ๐๐๐๐จ๐ฆ (๐๐๐ ) defined in Finite Element Analysis (๐ ๐๐)?
In FEA, Degrees of Freedom refers to the number of independent ways a node or element can move in a system. The DOF determines how the structure deforms under applied loads and boundary conditions.
โ๏ธ DOF in Structural Analysis โฆฟ In structural mechanics, DOFs are typically associated with displacements and rotations at each node: โฆฟTranslational DOF: Movement in the x, y, z directions. โฆฟ Rotational DOF: Rotation about the x, y, z axes.
For example: โฆฟ 1D elements (Beam, Truss): Can have 1 to 6 DOFs per node depending on the type. โฆฟ 2D elements (Shells, Membranes): Typically have 3 to 6 DOFs per node. โฆฟ 3D elements (Solid elements): Usually have 3 DOFs per node (translations in x,y,z).
โ๏ธ DOF in Different FEA Elements โฆฟ Truss Element - 3 (Translation in x,y,z) โฆฟ Beam Element - 6 (Translation + Rotation in x,y,z) โฆฟ Shell Element - 6 (3 Translation + 3 Rotation) โฆฟ Solid Element (3D Brick/Tetrahedral) - 3 (Translation in x,y,z).
โ๏ธ Importance of DOF in FEA โฆฟ Determines the stiffness matrix size. โฆฟ Affects computational complexity. โฆฟ Governs the accuracy of results (more DOF = higher accuracy but increased computation time).
โ๏ธ How DOF Affects Stiffness Matrix Size โฆฟ The total number of DOFs in the system (n) is determined by: n = (Number of nodes)ร(DOFs per node). Since the stiffness matrix is always square, its size is: (nรn)
โ๏ธ Why 3๐ ๐๐จ๐ฅ๐ข๐ Elements Have ๐๐ก๐ซ๐๐ ๐๐ซ๐๐ง๐ฌ๐ฅ๐๐ญ๐ข๐จ๐ง DOF ?
๐ก 3D solid elements, such as tetrahedra and hexahedra, have three translational DOFs per node (X, Y, Z) and no rotational DOFs. They capture material deformation using displacement gradients, making explicit rotational DOFs unnecessary. Rotational effects emerge naturally within the strain tensor. Unlike beams or shells, solid elements model bulk materials where deformations like stretching, compression, and shear are fully described by translations.
๐ก The stress-strain relationship is computed through nodal displacements, ensuring accurate structural behavior representation. Since solid elements lack thin surfaces or rotational axes, bending and twisting are indirectly captured as internal strain variations within the material.
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