Formulae for determining Green strain of an initially curved and twisted rod with circular cross-sections are derived by using the natural (curvilinear) coordinate system. Finite element analyses are performed for the...Formulae for determining Green strain of an initially curved and twisted rod with circular cross-sections are derived by using the natural (curvilinear) coordinate system. Finite element analyses are performed for the flexural buckling of initially curved and twisted thin rods under simultaneous action of axial force and torque. Numerical examples demonstrate that the given formulae are correcte. Some numerical results are compared with existing analytical solutions and data obtained by commercial FE software. The convergence of the proposed curved element is better than that of elements in the commercial FE software. It is shown that good accuracy and convergency are achieved by solving three-dimensional problems.展开更多
The group G of general coordinate transformations on the thermodynamic configuration space ε spanned by all the extensive variables keeps the first law of thermodynamics invariant. One can introduce a metric with Lor...The group G of general coordinate transformations on the thermodynamic configuration space ε spanned by all the extensive variables keeps the first law of thermodynamics invariant. One can introduce a metric with Lorentzian signature on the space ε, with the corresponding line element also being invariant under the action of G. This line element is identi6ed as the square of the proper entropy. Thus the second law of thermodynamics is also formulated invariantly and this lays down the foundation for the principle of thermal relativity.展开更多
A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative ...A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative entries that can occur in A whenever Ak≤0. Finally, we give a necessity and sufficiency condition for A2≤0.展开更多
文摘Formulae for determining Green strain of an initially curved and twisted rod with circular cross-sections are derived by using the natural (curvilinear) coordinate system. Finite element analyses are performed for the flexural buckling of initially curved and twisted thin rods under simultaneous action of axial force and torque. Numerical examples demonstrate that the given formulae are correcte. Some numerical results are compared with existing analytical solutions and data obtained by commercial FE software. The convergence of the proposed curved element is better than that of elements in the commercial FE software. It is shown that good accuracy and convergency are achieved by solving three-dimensional problems.
基金Supported by the National Natural Science Foundation of China under Grant No.10875059
文摘The group G of general coordinate transformations on the thermodynamic configuration space ε spanned by all the extensive variables keeps the first law of thermodynamics invariant. One can introduce a metric with Lorentzian signature on the space ε, with the corresponding line element also being invariant under the action of G. This line element is identi6ed as the square of the proper entropy. Thus the second law of thermodynamics is also formulated invariantly and this lays down the foundation for the principle of thermal relativity.
基金Supported by Shanxi Natural Science Foundation(20011006)
文摘A matrix whose entries are +,-, and 0 is called a sign pattern matrix. Let k be arbitrary positive integer. We first characterize sign patterns A such that .Ak≤0. Further, we determine the maximum number of negative entries that can occur in A whenever Ak≤0. Finally, we give a necessity and sufficiency condition for A2≤0.
