We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain： not just the material values and applied loads, but also the positions of the nodes are assumed ...We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain： not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening （pruning） technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.展开更多
Let （R, A） be a commutative form ring. We obtain a complete description of all subgroups of quadratic groups Q2n（R, A） which are normalized by elementary subgroups by form ideals, rather than usual ideals. For the...Let （R, A） be a commutative form ring. We obtain a complete description of all subgroups of quadratic groups Q2n（R, A） which are normalized by elementary subgroups by form ideals, rather than usual ideals. For the weak sandwich theorem, we give a direct proof without using localization method.展开更多
文摘We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain： not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening （pruning） technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.
基金supported by National Natural Science Foundation of China(Grant No.10871011)
文摘Let （R, A） be a commutative form ring. We obtain a complete description of all subgroups of quadratic groups Q2n（R, A） which are normalized by elementary subgroups by form ideals, rather than usual ideals. For the weak sandwich theorem, we give a direct proof without using localization method.
