Spatial Solid Analysis Using 8-Node Hexahedral Element (Hexahedral3D8Node)

The hexahedral element is one of the most commonly used element types in three-dimensional finite element analysis, particularly suitable for mechanical analysis of regular geometric bodies. Hexahedral3D8Node represents an 8-node hexahedral element where each node possesses three degrees of freedom in three-dimensional space (typically displacements in the x, y, and z directions).

In spatial solid analysis, this element can simulate complex three-dimensional stress-strain states. The core implementation involves constructing the element stiffness matrix, which describes the internal displacement field through shape functions and derives from material constitutive relationships (such as linear elastic models). A key implementation detail is the use of isoparametric formulation, where shape functions (often Lagrange polynomials) map local coordinates to global coordinates. Each node's displacement influences the entire element's deformation behavior through these shape functions, with the stiffness matrix computed using Gaussian integration over the element volume.

The analysis workflow generally includes: element discretization, stiffness matrix assembly, boundary condition application, and linear equation system solution. The hexahedral element's advantage lies in its higher computational accuracy and effective simulation of real-world 3D structures like mechanical components and building foundations. However, mesh quality must be carefully considered to avoid distorted elements that may lead to result inaccuracies. For nonlinear problems, extension to handle material nonlinearity or geometric nonlinearity requires additional implementation considerations, such as iterative solution methods and tangent stiffness matrix updates.