Pansystems logic conservation of bifurcation,catastrophe, chaos and stability

It is in references[4,5]that the combination of the relative researches of pansystems methodology and the researches of bifurcation,catastrophe,chaos and stability in nonlinear mechanics was put forward and the concepts were redefined from the point of view of pansystems methodology.The present paper studies the logic conservation law of these nonlinear mechanics phenomena under the framework of pansystems methodology.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM) AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICINE AND STRATEGICS(Ⅰ)

A new type of philosophy and mathematics from the pansystems view isintroduced here,including the7 philosophic theories(7PT)and related mathematicresearches.Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM)AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICIEN AND STRATEGICS(Ⅱ)

A new type of philosophy and mathematics from the pansystems view is introduced here, including the 7 philosophy theories (7PT) and related mathematizing researches. Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

Non-Gaussian Response of MDOF Wind-Exposed Structures: Analysis by Bicorrelation Function and Bispectrum

Abstract. The influence of non-Gaussian modeling of the wind action on the response of MDOF structures is considered. Assuming the turbulence as a homogeneous Gaussian field, the wind action field is described by means of the correlation and bicorrelation functions. Once known the spectrum and the bispectrum (by Fourier transform), the same quantities of the structural response are obtained by frequency domain analysis. This allows to evaluate the statistic moments of the response until the third moment and to estimate the peak value distribution. The procedure is applied to analyze a broadcasting antenna. Varying the structural damping and the wind characteristics, a comparison between Gaussian and non-Gaussian modeling is performed.Sommario. Viene studiata l'influenza della modellazione non-Gaussiana dell'azione del vento sulla risposta di strutture a più gradi di libertà. Considerando la turbolenza come un campo Gaussiano omogeneo, l'azione del vento viene descritta mediante le funzioni correlazione e bicorrelazione. Determinato poi lo spettro ed il bispettro (mediante trasformata di Fourier), le stesse grandezze relative alla risposta strutturale sono ricavate per mezzo dell'analisi nel dominio delle frequenze. È così possibile valutare i momenti statistici della risposta fino al terzo ordine e stimare la distribuzione dei valori di picco. La procedura viene applicata all'analisi della risposta di un'antenna per telecomunicazioni. Variando lo smorzamento strutturale e le caratteristiche del vento, vengono paragonate fra loro la modellazione Gaussiana e quella non-Gaussiana.     

A geometrically exact Cosserat shell-model including size effects,avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus

This contribution is concerned with a consistent formal dimensional reduction of a previously introduced finite-strain three-dimensional Cosserat micropolar elasticity model to the two-dimensional situation of thin plates and shells. Contrary to the direct modelling of a shell as a Cosserat surface with additional directors, we obtain the shell model from the Cosserat bulk model which already includes a triad of rigid directors. The reduction is achieved by assumed kinematics, quadratic through the thickness. The three-dimensional transverse boundary conditions can be evaluated analytically in terms of the assumed kinematics and determines exactly two appearing coefficients in the chosen ansatz. Further simplifications with subsequent analytical integration through the thickness determine the reduced model in a variational setting. The resulting membrane energy turns out to be a quadratic, elliptic, first order, non degenerate energy in contrast to classical approaches. The bending contribution is augmented by a curvature term representing an additional stiffness of the Cosserat model and the corresponding system of balance equations remains of second order. The lateral boundary conditions for simple support are non-standard. The model includes size-effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension and asymmetric shift of the midsurface. The formal thin shell membrane limit without classical h ³-bending term is non-degenerate due to the additional Cosserat curvature stiffness and control of drill rotations. In our formulation, the drill-rotations are strictly related to the size-effects of the bulk model and not introduced artificially for numerical convenience. Upon linearization with zero Cosserat couple modulus we recover the well known infinitesimal-displacement Reissner-Mindlin model without size-effects and without drill-rotations. It is shown that the dimensionally reduced Cosserat formulation is well-posed for positive Cosserat couple modulus by means of the direct methods of variations along the same line of argument which showed the well-posedness of the three-dimensional Cosserat bulk model [72].Received: 16 April 2004, Accepted: 3 May 2004, Published online: 17 September 2004