Abstract The classical Newton-Raphson (NR) method for solving nonlinear equations is
enhanced in two ways through the use of hypercomplex variables and algebra. In particular …

Damage tolerant design relies on accurately predicting the growth rate and path of fatigue
cracks under constant and variable amplitude loading. ANSYS Mechanical R19. 2 was used …

Solving transient heat transfer equations is required to understand the evolution of
temperature and heat flux. This physics is highly dependent on the materials and …

The hypercomplex finite element method, ZFEM, allows the analyst to compute highly-
accurate arbitrary-order shape, material property, and loading derivatives by augmenting the …

Phononic metamaterials (PMs) exhibit frequency ranges at which elastic waves are
attenuated called band gaps. However, this phenomenon is highly sensitive to geometrical …

Many modern structural health monitoring (SHM) systems use piezoelectric transducers to
induce and measure guided waves propagating in structures for structural damage …

The hypercomplex-variable finite element method, ZFEM, is extended to compute the mode I
and mode II energy release rates (ERR) for functionally graded materials. The ERR is …

Featured Application Sensitivity analysis of the modal response in structural systems.
Abstract The calculation of accurate arbitrary-order sensitivities of eigenvalues and …

This study presents a developed finite element code written by Visual Fortran to
computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant …

The sensitivity analysis of the anisotropic properties for PZT-4 and PZT-5 have been
performed using the complex variable finite element method (ZFEM) on a two-dimensional …