Geometrically nonlinear higher-gradient elasticity with energetic boundaries
نویسندگان
چکیده
منابع مشابه
Higher-order Gradient Elasticity Models Applied to Geometrically Nonlinear Discrete Systems
The buckling and post-buckling behavior of a nonlinear discrete repetitive system, the discrete elastica, is studied herein. The nonlinearity essentially comes from the geometrical effect, whereas the constitutive law of each component is reduced to linear elasticity. The paper primarily focuses on the relevancy of higher-order continuum approximations of the difference equations, also called c...
متن کاملFirst-Order System Least Squares for Geometrically Nonlinear Elasticity
Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. In this thesis, we develop a first-order system least-squares (FOSLS) method to approximate the solution to the equations of geometrically-nonlinear elasticity in two dimensions. We con...
متن کاملInjectivity and Self-Contact in Second-Gradient Nonlinear Elasticity
We prove the existence of globally injective weak solutions in mixed boundary-value problems of second-gradient nonlinear elastostatics via energy minimization. This entails the treatment of self-contact. In accordance with the classical (first-gradient) theory, the model incorporates the unbounded growth of the potential energy density as the local volume ratio approaches zero. We work in a cl...
متن کاملEnergetic Natural Gradient Descent
In this appendix we show that 1 2 ∆ F (θ)∆ is a second order Taylor approximation of D KL (p(θ)p(θ + ∆)). First, let g q (θ) :=D KL (qp(θ)) = ω∈Ω q(ω) ln q(ω) p(ω|θ). We begin by deriving equations for the Jacobian and Hessian of g q at θ: ∂g q (θ) ∂θ = ω∈Ω q(ω) p(ω|θ) q(ω) ∂ ∂θ q(ω) p(ω|θ) = ω∈Ω q(ω) p(ω|θ) q(ω) −q(ω) ∂p(ω|θ) ∂θ p(ω|θ) 2 = ω∈Ω − q(ω) p(ω|θ) ∂p(ω|θ) ∂θ , (4) and so: ∂ 2 g q (θ)...
متن کاملEnergetic Natural Gradient Descent
We propose a new class of algorithms for minimizing or maximizing functions of parametric probabilistic models. These new algorithms are natural gradient algorithms that leverage more information than prior methods by using a new metric tensor in place of the commonly used Fisher information matrix. This new metric tensor is derived by computing directions of steepest ascent where the distance ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mechanics and Physics of Solids
سال: 2013
ISSN: 0022-5096
DOI: 10.1016/j.jmps.2013.06.005