Meaning
Numerical method used in finite element analysis to estimate values at any point within an element based on the known values at the nodes. Shape function interpolation defines how variables like displacement or pressure vary across the geometry of a simulated plastic part. This mathematical bridge allows a continuous physical system to be represented by a discrete mesh.
It is the core mechanism that enables the prediction of stress concentrations and deformation in complex moulded geometries.
Element Order
Choice of interpolation function determines the accuracy of the results and the computational cost. Linear shape functions assume a constant gradient across the element, while quadratic functions allow for curved deformation patterns. For parts with tight radii or high stress gradients, higher-order elements are necessary to avoid artificially stiff results.
Consistency Check
Sum of the shape functions at any point inside the element must always equal one. This property ensures that the interpolated field is continuous and that the model can represent rigid-body motion correctly. If the functions are not properly defined, the simulation may fail to converge or produce physically impossible results.
Mapping Accuracy
Distortion of the element shape during meshing can degrade the quality of the interpolation.
