A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergenc...A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.展开更多
A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-or...A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.展开更多
In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. T...In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.展开更多
When pointed V-notches weaken structural components, local stresses are singular and their intensities are expressed in terms of the notch stress intensity factors (NSIFs). These parameters have been widely used for...When pointed V-notches weaken structural components, local stresses are singular and their intensities are expressed in terms of the notch stress intensity factors (NSIFs). These parameters have been widely used for fatigue assessments of welded struc- tures under high cycle fatigue and sharp notches in plates made of brittle materials subjected to static loading. Fine meshes are required to capture the asymptotic stress distributions ahead of the notch tip and evaluate the relevant NSIFs. On the other hand, when the aim is to determine the local Strain Energy Density (SED) averaged in a control volume embracing the point of stress singularity, refined meshes are, not at all, necessary. The SED can be evaluated from nodal displacements and regular coarse meshes provide accurate values for the averaged local SED. In the present contribution, the link between the SED and the NSIFs is discussed by considering some typical welded joints and sharp V-notches. The procedure based on the SED has been also proofed to be useful for determining theoretical stress concentration factors of blunt notches and holes. In the second part of this work an application of the strain energy density to the fatigue assessment of A17075 notched plates is presented. The experimental data are taken from the recent literature and refer to notched specimens subjected to different shot peening treatments aimed to increase the notch fatigue strength with respect to the parent material.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12072302 and 11772280)the Natural Science Foundation of Fujian Province of China (Grant No.2021J02003).
文摘A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines,which reveals an interesting coarse mesh superconvergence.Firstly,the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived,where the degeneration to Timoshenko beams is discussed as well.Subsequently,in accordance with these frequency error measures,the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration.On the other hand,the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy.Meanwhile,it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates,in comparison with the ultimate fourth order accuracy as the meshes are progressively refined.Furthermore,the mesh size threshold for the coarse mesh superconvergence is provided as well.The proposed theoretical results are consistently proved by numerical experiments.
基金Supported by National Science Foundation of China(Grant 10871179)the National Basic Research Programme of China(Grant 2008CB717806)the Department of Education of Zhejiang Province(GrantY200803559).
文摘A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.
基金The project was supported by National Science Foundation (Grant No. 10471129).
文摘In this paper we propose the finite difference method for the forward-backward heat equation. We use a coarse-mesh second-order central difference scheme at the middle line mesh points and derive the error estimate. Then we discuss the iterative method based on the domain decomposition for our scheme and derive the bounds for the rates of convergence. Finally we present some numerical experiments to support our analysis.
基金supported by the Italian Research Program(Grant No.CPDA100715)entitled"Static and fatigue behaviour of structural notched components subjected to tension and torsion under small or large scale yielding"the Italian PRIN project(Grant No.2009Z55NWC_001)
文摘When pointed V-notches weaken structural components, local stresses are singular and their intensities are expressed in terms of the notch stress intensity factors (NSIFs). These parameters have been widely used for fatigue assessments of welded struc- tures under high cycle fatigue and sharp notches in plates made of brittle materials subjected to static loading. Fine meshes are required to capture the asymptotic stress distributions ahead of the notch tip and evaluate the relevant NSIFs. On the other hand, when the aim is to determine the local Strain Energy Density (SED) averaged in a control volume embracing the point of stress singularity, refined meshes are, not at all, necessary. The SED can be evaluated from nodal displacements and regular coarse meshes provide accurate values for the averaged local SED. In the present contribution, the link between the SED and the NSIFs is discussed by considering some typical welded joints and sharp V-notches. The procedure based on the SED has been also proofed to be useful for determining theoretical stress concentration factors of blunt notches and holes. In the second part of this work an application of the strain energy density to the fatigue assessment of A17075 notched plates is presented. The experimental data are taken from the recent literature and refer to notched specimens subjected to different shot peening treatments aimed to increase the notch fatigue strength with respect to the parent material.