The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, an...The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.展开更多
The paper is a contribution to the technical discussion concerning the collapses of the WTC buildings. It returns to the problem of the dynamics of the collapses;it does not concern the reason why the buildings starte...The paper is a contribution to the technical discussion concerning the collapses of the WTC buildings. It returns to the problem of the dynamics of the collapses;it does not concern the reason why the buildings started collapsing, but investigates the dynamics of the collapse itself. It works with the same assumptions as the official NIST report [1], i.e. that the falling mass hits the motionless mass beneath;the supporting columns loose stability and the mass of the pertinent floor starts to fall together with the falling mass. The aim was to derive the theoretical upper limit of the speed of the collapse, supposing that influence of the columns which resist the fall, is neglected. The differential equation of the fall was obtained using two independent laws of mechanics, with the identical result. Its solution can be found from a very simple explicit formula. The theoretical upper limit acceleration of the fall obtained by such formula is one third of the gravitational acceleration, which is faster than it was observed in the case of the collapses of WTC1 and WTC2. This leads to the conclusion that the mechanism of the collapse must be different from the assumed and the falling mass must not hit the motionless mass bellow it, but rather a mass which had started to fall before the impact of the falling mass occurred.展开更多
文摘The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.
基金supported from the project of Ministry of Educa-tion,Youth and Sports of the Czech Republic AdMaS UP(Advanced Materials,Structures and Technologies),National Sustainability Programme I,LO1408.
文摘The paper is a contribution to the technical discussion concerning the collapses of the WTC buildings. It returns to the problem of the dynamics of the collapses;it does not concern the reason why the buildings started collapsing, but investigates the dynamics of the collapse itself. It works with the same assumptions as the official NIST report [1], i.e. that the falling mass hits the motionless mass beneath;the supporting columns loose stability and the mass of the pertinent floor starts to fall together with the falling mass. The aim was to derive the theoretical upper limit of the speed of the collapse, supposing that influence of the columns which resist the fall, is neglected. The differential equation of the fall was obtained using two independent laws of mechanics, with the identical result. Its solution can be found from a very simple explicit formula. The theoretical upper limit acceleration of the fall obtained by such formula is one third of the gravitational acceleration, which is faster than it was observed in the case of the collapses of WTC1 and WTC2. This leads to the conclusion that the mechanism of the collapse must be different from the assumed and the falling mass must not hit the motionless mass bellow it, but rather a mass which had started to fall before the impact of the falling mass occurred.
