TY - JOUR

T1 - Asymptotics of the deflection of a cruciform junction of two narrow Kirchhoff plates

AU - Nazarov, S.A.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation, project no. 17-11-01003.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - Abstract: Two two-dimensional plates with bending described by Sophie Germain’s equation with the biharmonic operator are joined in the form of a cross with clamped ends, but with free lateral sides outside the cross core. Asymptotics of the deflection of the junction with respect to the relative width of the plates regarded as a small parameter is constructed and justified. The variational-asymptotic model includes a system of two ordinary differential equations of the fourth and second orders with Dirichlet conditions at the endpoints of the one-dimensional cross and the Kirchhoff transmission conditions at its center. They are derived by analyzing the boundary layer near the crossing of the plates and mean that the deflection and the angles of rotation at the central point are continuous and that the total bending force and the principal torques vanish. Possible generalizations of the asymptotic analysis are discussed.

AB - Abstract: Two two-dimensional plates with bending described by Sophie Germain’s equation with the biharmonic operator are joined in the form of a cross with clamped ends, but with free lateral sides outside the cross core. Asymptotics of the deflection of the junction with respect to the relative width of the plates regarded as a small parameter is constructed and justified. The variational-asymptotic model includes a system of two ordinary differential equations of the fourth and second orders with Dirichlet conditions at the endpoints of the one-dimensional cross and the Kirchhoff transmission conditions at its center. They are derived by analyzing the boundary layer near the crossing of the plates and mean that the deflection and the angles of rotation at the central point are continuous and that the total bending force and the principal torques vanish. Possible generalizations of the asymptotic analysis are discussed.

KW - Kirchhoff transmission conditions

KW - asymptotics

KW - boundary layer

KW - cruciform junction of narrow plates

KW - one-dimensional model

UR - http://www.scopus.com/inward/record.url?scp=85052241693&partnerID=8YFLogxK

U2 - 10.1134/S0965542518070138

DO - 10.1134/S0965542518070138

M3 - Article

VL - 58

SP - 1150

EP - 1171

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 7

ER -