A convolutional-iterative solver for nonlinear dynamical systems

Nonlinear convolution finite element method for solution of large deformation elastodynamics

“…In the numerical implementations, the notion of inifinity in the above equation is realized by considering a large number, say N − 1. Now, following the similar manupulations represented in [24], one can find the m th iteration, which is equivalent to (4.4), as follows:…”

“…Also, it has been demonstrated in a number of works that the framework can be developed for various types of physical processes (see [20,21,22,23], among others). Recently, based on the alternative form and similar approach established in [19], a nonlinear solver has been developed for nonlinear dynamical systems in [24]. These desired characteristics motivated us to develop a dynamic nonlinear finite element scheme for nonlinear elastodynamics involving geometrical and material nonlinearities.…”

Convolution finite element method for analysis of piezoelectric materials

“…Similar variational formulations for electromagneto-elasticity have been established in [29]. Recently, a similar approach has been followed in [30] for a class of nonlinear dynamical systems in which the method, in contrast to the Newmark average acceleration method, adaptively conserves the constants of motion. Hence, it is advantageous to introduce such methods for the case of piezoelectric (piezomagnetic) materials.…”