Accurate fracture analysis of multi-material V-notched Reissner plates under bending or twisting

Abstract

An accurate fracture analysis of multi-material V-notched Reissner plates under bending or twisting is performed by a new coupling approach of isogeometric analysis (IGA) and eigenfunction expansion method. In this approach, the overall plate is divided into two regions: a singular region near the notch tip (near field) and a regular region far away from the notch tip (far field). The overall model is discretized by a T-spline-based IGA. Asymptotic solutions of singular stress fields are applied to the near field, and therefore, the large number of fundamental unknowns of control points is reduced into a small set of undetermined coefficients. The unknowns in the far field remain unchanged. Consequently, the computational cost is significantly reduced, and explicit expressions of singular stress components in the vicinity of notch tip are obtained without post processing. Comparisons are presented to demonstrate the accuracy and convergence of the present approach. Effects of key influencing factors on the singularity order and singular items of stresses are investigated also.

Analysis on scattering characteristics of SH guided wave due to V-notch in a piezoelectric bi-material strip

“…The coefficients in the system of linear integral equations are as follows: 11) n exp ( À iqu)du, j (14) nq = ð Àp=2 Àp j (14) n exp ( À iqu)du, j (21) nq = ð Àp=2 Àp j (21) n exp ( À iqu)du, j (22) nq = ð Àp=2 Àp j (22) n exp ( À iqu)du, j (23) nq = ð Àp=2 Àp j (23) n exp ( À iqu)du, j (24) nq = ð Àp=2 Àp j (24) n exp ( À iqu)du, j…”

“…By the tests on a notched plate, Rahaman [20] used Gridap-based phase-field Julia code to simulate fracture in brittle materials. Yu et al [21] performed an accurate fracture analysis of multi-material V-notched Reissner plates under bending or twisting. Based on Kolosov–Muskhelishvili’s approach, Alavi et al [22] developed an analytical stress solution for the bi-material V-notches with an end hole (VO).…”