in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.

In this paper we present a meshfree discretization technique based only on a set of irregularly spaced points xi ∈ IRd and the partition of unity approach. In this sequel to [13] we focus on the cover construction and its interplay with the integration problem arising in a Galerkin discretization. We present a hierarchical cover construction algorithm and a reliable decomposition quadrature sch...

In prior work, we extended the well-known form closure grasp framework for rigid parts to a class of deformable parts, modeled as frictionless polygons with a finite element mesh and given stiffness matrix. We define the D-space (deformationspace) of a part as the C-space of all its mesh nodes and deform closure in terms of the work needed to release the part from a set of finger contacts. In t...

We study the condition number of the stiffness matrix arising from finite element discretizations of nonlocal integral operators with singular and integrable kernels. Such operators are used in nonlocal diffusion, peridynamics formulation of continuum mechanics, image processing, and phase transition. We quantify of the extremal eigenvalues with respect to all underlying parameters; the horizon...

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a rel...

Simple and economical procedures for large-deformation elasto-plastic analysis of frames, whose members can be characterized as beams, are presented. An assumed stress approach is employed to derive the tangent stiffness of the beam, subjected in general to non-conservative type distributed loading. The beam is assumed to undergo arbitrarily large rigid rotations but small axial stretch and rel...

The dynamic behavior of railway bridges carrying high-speed trains can be analyzed with or without the consideration of the vehicle's own structure. However, due to the amount of kinetic energy carried at high speeds, the train may interact significantly with the bridge, especially when resonance occurs. Equally important is the riding comfort and the stability of the track and train cars, whic...

Rotating beams are considerably used in different mechanical and aeronautical installations. In this paper, free vibration of non-prismatic rotating Euler-Bernoulli beams is studied. Dynamic stiffness matrix is evaluated by using differential transform method, a powerful numerical tool in solution of ordinary differential equations, for solving the governing equation of motion. The method is ca...

We present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is sol...

Green’s functions are important mathematical tools in mechanics and in other parts of physics. For instance, the boundary element method needs to know the Green’s function of the problem to compute its numerical solution. However, Green’s functions are only known in a limited number of cases, often under the form of complex analytical expressions. In this article, a new method is proposed to ca...