Meaning
Mathematical translation of field variables across discrete element nodes enables continuous mapping of strain, stress and thermal gradients in finite element analysis models. Implementing shape-function mesh interpolation allows simulation software to evaluate localized melt pressure and shrinkage variations across intricate mold geometries. This numerical technique operates within spatial element domains, losing validity where element distortion creates singular geometric transformations or invalid Jacobians.
Field Mapping
Polynomial functions map nodal displacements to continuous displacement fields within triangular, quadrilateral or hexahedral elements. In process modeling, shape-function mesh interpolation calculates velocity and temperature profiles across thin cavity cross-sections during injection mold filling. Higher-order shape functions accommodate steep thermal gradients near mold walls, preventing numerical dispersion during thermal analysis.
Inappropriate element formulation leads to shear locking, yielding artificial stiffness in thin-walled structural simulations.
Remeshing Accuracy
Transferring state variables between non-matching computational grids becomes necessary when simulating large deformations or dynamic mold filling. During adaptive mesh refinement, shape-function mesh interpolation transfers fiber orientation tensors from flow analysis meshes onto structural analysis meshes. Inaccurate interpolation introduces smoothing errors that underestimate localized stress concentrations at rib intersections or wall thickness transitions.
Simulation engineers adjust polynomial orders to maintain energy conservation across mesh interfaces.
Convergence Behavior
Numerical accuracy depends directly on element distortion and nodal distribution across the geometrical domain. Distorted elements degrade the precision of shape-function mesh interpolation, introducing artificial strain energy and slowing solver convergence. Higher mesh density in gate regions and sharp radii reduces interpolation error, ensuring realistic predictions of residual stresses and part warpage.
Validating simulation results against physical molded part measurements requires verifying mesh independence across critical geometry zones.
