86 research outputs found
Π Π²Π»ΠΈΡΠ½ΠΈΠΈ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΡΡ ΠΈ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΠΊΠΎΠ½ΡΠ΅Π²ΡΡ ΡΡΠ΅Π· Π½Π° Π²ΠΈΠ±ΡΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΡΠ΅Π·Π΅ΡΠΎΠ²Π°Π½ΠΈΡ
Π ΡΡΠ°ΡΡΠ΅ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ Π°Π½Π°Π»ΠΈΠ· ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΡΡ
ΠΈ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΊΠΎΠ½ΡΠ΅Π²ΡΡ
ΡΡΠ΅Π·, Π²ΠΈΠ΄ΠΎΠ² ΡΠ°Π±ΠΎΡ, Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΠΌΡΡ
ΠΊΠΎΠ½ΡΠ΅Π²ΡΠΌΠΈ ΡΠΈΠ»ΠΈΠ½Π΄ΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΡΡΠ΅Π·Π°ΠΌΠΈ. ΠΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½ΠΎ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΡΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π½Π° Π²ΠΈΠ±ΡΠΎΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΡΠ΅Π·Π΅ΡΠΎΠ²Π°Π½ΠΈΡ.This article gives an analysis of the structural and geometric parameters of end mills, types of work performed by the cylindrical end mills. The effect of these parameters on the vibration milling process
The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry
The closest tensors of higher symmetry classes are derived in explicit form
for a given elasticity tensor of arbitrary symmetry. The mathematical problem
is to minimize the elastic length or distance between the given tensor and the
closest elasticity tensor of the specified symmetry. Solutions are presented
for three distance functions, with particular attention to the Riemannian and
log-Euclidean distances. These yield solutions that are invariant under
inversion, i.e., the same whether elastic stiffness or compliance are
considered. The Frobenius distance function, which corresponds to common
notions of Euclidean length, is not invariant although it is simple to apply
using projection operators. A complete description of the Euclidean projection
method is presented. The three metrics are considered at a level of detail far
greater than heretofore, as we develop the general framework to best fit a
given set of moduli onto higher elastic symmetries. The procedures for finding
the closest elasticity tensor are illustrated by application to a set of 21
moduli with no underlying symmetry.Comment: 48 pages, 1 figur
Guidelines and Recommendations on the Use of Higher OrderFinite Elements for Bending Analysis of Plates
This paper compares and evaluates various plate finite elements to analyse the static response of thick and thin plates subjected to different loading and boundary conditions. Plate elements are based on different assumptions for the displacement distribution along the thickness direction. Classical (Kirchhoff and Reissner-Mindlin), refined (Reddy and Kant), and other higher-order displacement fields are implemented up to fourth-order expansion. The Unified Formulation UF by the first author is used to derive finite element matrices in terms of fundamental nuclei which consist of 3 Γ 3 arrays. The MITC4 shear-locking free type formulation is used for the FE approximation. Accuracy of a given plate element is established in terms of the error vs. thickness-to-length parameter. A significant number of finite elements for plates are implemented and compared using displacement and stress variables for various plate problems. Reduced models that are able to detect the 3D solution are built and a Best Plate Diagram (BPD) is introduced to give guidelines for the construction of plate theories based on a given accuracy and number of terms. It is concluded that the UF is a valuable tool to establish, for a given plate problem, the most accurate FE able to furnish results within a certain accuracy range. This allows us to obtain guidelines and recommendations in building refined elements in the bending analysis of plates for various geometries, loadings, and boundary conditions
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