Search results for "Tangent"

Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals

2012

Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.

A thermodynamic approach to nonlocal plasticity and related variational principles

1999

Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …

A FE-Meshless Multiscale Approach for Masonry Materials

2015

Abstract A FE-Meshless multiscale computational strategy for the analysis of running bond masonry is presented. The Meshless Method (MM) is adopted to solve the boundary value problem (BVP) at the mesoscopic level. The representative unit cell is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter are simulated as non-associated elastic-plastic zero-thickness interfaces with a softening response. Macroscopic localization of plastic bands is obtained performing a spectral analysis of the tangent stiffness matrix. Localized plastic bands are embedded into the quadrature points area of the macroscopic finite elements.

CH of masonry materials via meshless meso-modeling

2014

In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Meth…

The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two

1997

In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.

The Tangentenflügel and Other Pianos with Non-Pivoting Hammers

2008

On the volume of unit vector fields on spaces of constant sectional curvature

2004

A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.

The forgotten mathematical legacy of Peano

2019

International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.

Reduction to finite dimensions of continuous systems having only a few amplified modes

2008

In the approach of Guckenheimer and Knobloch the amplitudes of trajectories on the unstable manifold 0 are the pivotal quantities. This places a certain restriction on the applicability of this approach, as only neighbourhoods of 0 of the unstable manifold of 0 are accessible, which have a one-to-one projection into their tangent at 0, the linear space spanned by the amplified modes. This restriction may be lifted, using the arc lengths of trajectories instead.

A Consistent Boundary/Interior Element Method for Evolutive Elastic Plastic Structural Analysis

1993

A symmetric/sign-definite formulation of the BEM to address the evolutive elastic plastic analysis of structures is presented. A wide class of material models with internal variables and thermodynamic potential is considered. Different energy methods—namely the boundary min-max principle, the Helmholtz free energy and the maximum intrinsic dissipation theorem—axe employed in order to provide the discretization operations by boundary elements and cell elements with inherent variational consistency. The resulting space-discretized equations can be solved by a step-by-step procedure and a predictor/corrector iteration scheme, with corrections operated locally cell-by-cell, just as with the FEM…