In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate example...In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.展开更多
In 4-dimensional R-gravity, using the linear and square terms of the expanding expression of the space-time connection, we calculate the possible curvature excitation （order k^4） of gravitational field, which is giv...In 4-dimensional R-gravity, using the linear and square terms of the expanding expression of the space-time connection, we calculate the possible curvature excitation （order k^4） of gravitational field, which is given by the first term of quantum Wilson loop （w） through two-point Green＇s function of the connection. At the same time using the tree diagram propagators of gravitons, the lowest order （k^4） correction to （w） is also calculated through the graviton self-energy in the term. Under the accuracy condition up to order k^4, we have obtained a complete expression of the excitation contributed from the leading term （w^（2））of （w）.展开更多
基金The project was supported by the National Natural Science Foundation of China(11001037,11102037,11072156)the Fundamental Research Funds for the Central Universities of China(DUT10ZD112,DUT10JS02)
文摘In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.
基金The project partially supported by Fund of the Education Department of Hubei Province of China under Grant No. D200534001
文摘In 4-dimensional R-gravity, using the linear and square terms of the expanding expression of the space-time connection, we calculate the possible curvature excitation （order k^4） of gravitational field, which is given by the first term of quantum Wilson loop （w） through two-point Green＇s function of the connection. At the same time using the tree diagram propagators of gravitons, the lowest order （k^4） correction to （w） is also calculated through the graviton self-energy in the term. Under the accuracy condition up to order k^4, we have obtained a complete expression of the excitation contributed from the leading term （w^（2））of （w）.
