Matrix and Finite Element Displacement Analysis of Structures

Nonlocal Modal Analysis for Nanoscale Dynamical Systems

“…For the special case when the rod is local, the mass matrix derived above reduces to the classical mass matrix [34,35] as e 0 a = 0 . Therefore for a nonlocal rod, the element stiffness matrix is identical to that of a classical local rod but the element mass has an additive term which is dependent on the nonlocal parameter.…”

“…Using this, the stiffness matrix can be obtained using the conventional variational formulation [35] as The mass matrix for the nonlocal element can be obtained as For the special case when the beam is local, the mass matrix derived above reduces to the classical mass matrix [34,35] as e 0 a = 0.…”

Generating Realistic Facial Expressions with Wrinkles for Model-Based Coding

“…According to the principle of minimum potential energy, of all possible kinematically admissible displacement configurations that an elastic body can take up, the configuration which satisfies equilibrium makes the total potential energy assume a minimum value [9]. The potential energy stated in the principle of minimum potential energy includes the strain energy and the potential energy formed by external forces.…”

A family of 13-node plate bending triangular elements

“…However, there are incompatible elements with discontinuous derivatives, which yield acceptable results. 2 In this paper, several high-order elements are presented. Some of these elements have been introduced and evaluated by other investigators.…”