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type, title, complexity, domain, aliases, created, updated, address, tags, status, related, sources
| type | title | complexity | domain | aliases | created | updated | address | tags | status | related | sources | |||||||||
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| concept | Isoparametric Linear Solid Elements | intermediate | computational-mechanics |
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2026-05-28 | 2026-05-28 | c-000049 |
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current |
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Isoparametric Linear Solid Elements
Definition
Isoparametric linear solid elements are first-order three-dimensional continuum finite elements that interpolate both geometry and displacement with the same nodal shape functions.
How They Work
The source treats solid elements as volume elements with three translational displacement degrees of freedom per node: u, v, and w. They do not include rotational degrees of freedom, so connecting them directly to beam, plate, or shell elements can require care to avoid singular constraints.
The physical position and displacement field are both interpolated from nodal values:
x(xi) = sum N_i(xi) x_i
u(xi) = sum N_i(xi) u_i
The covered topologies are 4-node tetrahedron, 5-node pyramid, 6-node wedge, and 8-node hexahedron. In each case, the element is defined in natural coordinates and mapped to physical space through the Jacobian.
Practical Notes
- Solid elements are suited to three-dimensional volume response rather than beam or shell idealizations.
- Aspect ratios close to one are preferred because distortion degrades the shape-function mapping and numerical integration quality.
- The absence of rotational degrees of freedom is a modeling interface issue when solid elements meet structural elements.
Connections
- Solid Element Shape Functions defines the natural-coordinate interpolation for each covered topology.
- Solid Element Strain-Displacement Matrix converts the displacement interpolation into engineering strain components.
- Solid Element Stiffness Integration assembles the stiffness matrix from
B,D, and the Jacobian.