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| 1 | 求解粘弹性问题的时域自适应等几何比例边界有限元法显示文摘提出一种基于分段时域自适应算法和等几何分析的求解粘弹性问题的数值方法。利用时域分段展开,建立了递推格式的比例边界元求解方程,环向比例边界采用等几何技术离散,在继承常规比例边界有限元半解析、便于处理应力奇异性/无限域问题等优点的同时,可更准确地描述几何边界,由此进一步提高了计算精度;在时域,通过分段时域自适应计算,保证不同时间步长下的计算精度。通过数值算例,从计算精度、收敛性等方面,对所提方法的有效性进行了验证。 | 何宜谦 王霄腾 祝雪峰 杨海天 薛齐文 | 2020 | 工程力学2020，37，2： | 4 |
| 2 | New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space显示文摘The two-dimensional(2D)transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method(SSM).The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented,which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods.The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions.The results obtained by the SSM agree well with those obtained from the finite element method(FEM),which confirms the accuracy of the SSM. | Dian XU Xinran ZHENG Dongqi AN Chao ZHOU Xiuwen HUANG Rui LI | 2022 | Applied Mathematics and Mechanics(English Edition)2022，43，8： | 0 |
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