A simple triangular shell finite element with fifteen degrees of freedom for the analysis of general shell structures is presented in this work. The element uses a substitute transverse shear strain field to avoid locking, and is formulated on the basis of RSDS-element (Resultant Stress Degenerated Shell Element) approach, which leads to very simple strain-displacement expressions. The substitu...

We develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. Also general meshes with polytopal element and hanging node can be used in the method. We prove that our finit...

Topics in Designing Low Thermal Expansion Lattices at the Microscale John Chu Master of Applied Science Graduate Department of Aerospace Science and Engineering University of Toronto 2011 Microscale bi-material lattices with near zero thermal expansion are designed to create a thermally stable optical surface for applications in a space telescope. To facilitate the design, the thermal expansion...

The third-order aberrations of a diffractive optical element with paraxial zone spacings are derived as a function of aperture stop position. It is shown that by placing the stop in the front focal plane, coma and astigmatism are identically zero, assuming an infinitely distant object. In addition, since the element is diffractive, the Petzval sum is also zero. Modulation transfer function comp...

The axisymmetric, compressible visco-resistive two-fluid plasma equations are examined under the constraint that the current is purely poloidal and the pressure is a function of density only (“barotropic”). For ideal plasmas (zero resistivity and zero viscosity) the Kelvin circulation theorem of fluid mechanics and the concept of frozen-in field lines turn out to be limiting cases of a more gen...

Let m ≥ 2 and k ≥ 2 be integers and let R be a commutative ring with a unit element denoted by 1. A k-th power diophantine m-tuple in R is an m-tuple (a1, a2, . . . , am) of non-zero elements of R such that aiaj +1 is a k-th power of an element of R for 1 ≤ i < j ≤ m. In this paper, we investigate the case when k ≥ 3 and R = K[X], the ring of polynomials with coefficients in a field K of charac...

Introduction. The object of this paper is to characterize the clans (compact connected Hausdorff topological semigroups with an identity element) which are homeomorphic to a unit interval and which have a nondegenerate kernel (minimal two-sided ideal). The corresponding case when the kernel is degenerate has been characterized in a paper by H. Cohen and L. I. Wade [2] together with an earlier p...

The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, ...

We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [2], which is a special case of Ericksen’s general continuum model in [5]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical full...