1,720,989 research outputs found
From Special Bounded Deformation to Special Bounded Hessian: the elastic-plastic beam
No full textQuad n.551/P, Dip.Matematica del Politecnico di Milan
Variational linearization of pure traction problems in incompressible elasticity
No full textWe consider pure traction problems, and we show that incompressible linearized elasticity can be obtained as variational limit of incompressible finite elasticity under suitable conditions on external loads
Sharp conditions for the linearization of finite elasticity
No full textWe consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can be strictly lower than the minimal value of the standard linear elastic energy if a strict compatibility condition for external loads does not hold. The results are provided for both the compressible and the incompressible case
Newton’s second law as limit of variational problems
No full textWe show that the solution of Cauchy problem for the classical ODE my′′= f can be obtained as the limit of minimizers of exponentially weighted convex variational integrals. This complements the known results about weighted inertia-energy approach to Lagrangian mechanics and hyperbolic equations
A variational approach to non linear elastic plates
No full textBy adopting the variational point of view, the constitutive equations of a non linear elastic plate are
deduced under kinematical constraints on the admissible deformations
Plastic hinges in a beam
No full textThis talk focuses on the minimization of 1 dimensional free discontinuity problem with second order energy dependent on jump integrals but not on the cardinality of the discontinuity set. Related energies, describing loaded elastic-plastic beams, are not lower semi continuous in BH (the space of displacements with second derivatives which are measures). Nevertheless we show that if a safe load condition is fulfilled then minimizers exist and they belong actually to SBH; say their second derivative has no Cantor part. If in addition a stronger condition on load is fulfilled then minimizer is unique and belongs to the Sobolev space H2. Moreover we can always select one minimizer whose number of plastic hinges does not exceed 2 and is the limit of minimizers of
penalized problems.
When the load stays in the gap between safe load and regularity condition then minimizers with hinges are allowed; if in addition the load is symmetric and strictly positive then there is uniqueness of minimizer, the hinges of such minimizer are exactly
two and they are located at the endpoints.
If the beam is under the action of a skew-symmetric load then the safe load condition is less stringent than in the general case
Elastic-brittle reinforcement of flexural structures
No full textThis note provides a variational description of the mechanical e¤ects of flexural sti¤ening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforce- ment is assumed to be linear elastic outside possible free plastic yield lines or free crack. Explicit Euler equations and a compliance identity are shown for the reinforcement of a 1D beam
Energy minimizing states in adhesion problems for elastic rods
No full textIn this paper we analyze and compare two different models for adhesion
phenomena, recently proposed by the authors. In the first approach
[9] a feasible expression of the adhesion energy is suggested by the existence
problem of partially detached equilibrium states. In the second
model [10] the macroscopic energy is obtained by performing a multiscale
analysis and it is deduced via a macroscopic Γ-limit of the energy
at the scale of the microstructure. Interestingly, we obtain that the first
model can be deduced by the second one as the limit case when the
parameter measuring the relative stiffness of the adhesive layer and the
beam diverges
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