Forms of stability loss of three-layer sheets and shells with external layers made of homogeneous or reinforced materials

A stability theory of sandwich structural elements 1. Analysis of the current state and a refined classification of buckling forms

“…In this connection, for sandwich and multi-layered shells with transversely soft fillers, belonging to the thin shells, a refined theory ofprt~ritical deformation and a linearized stability theory were constructed, which admits, contrary to the data presented in [13], a great index of variability of the tangential stresses in the fillers for a much more precise description of the SSS compared with [ 13] due to the introduction of merely two additional unknown functions for each layer of the filler. The accuracy of the equations of this theory, aS the investigations on the limits of their applicability have shown [21 ], practically approaches the accuracy of the linearized equations of the three-dimensional elaSticity theory in determining such integral characteristics as the critical load or the frequency of free vibrations of sandwich and multi-layered shells with transversely soft fillers.…”

“…(8) Table 2 shows the results of solution of the above problem obtained on the basis of the maximally simplified [13] and refined [ 17] equations at a fixed value of r= 5 and by varying the parameters ~p and k 13. In this table, m is the number of hal f-waves of stability loss appearing in Eqs.…”

“…It waS found in [14][15][16][17][18][19][20] that the equations used in [ 13] to examine the mixed FSL (based on the broken line-type model with account of the transverse compression) are maximally simplified. In this connection, for sandwich and multi-layered shells with transversely soft fillers, belonging to the thin shells, a refined theory ofprt~ritical deformation and a linearized stability theory were constructed, which admits, contrary to the data presented in [13], a great index of variability of the tangential stresses in the fillers for a much more precise description of the SSS compared with [ 13] due to the introduction of merely two additional unknown functions for each layer of the filler.…”

“…Taking into account the results of investigations dedicated to the statement and solution of stability problems of sandwich plates in transverse [11] and longitudinal-transverse bending [12], a refined classification of FSL of sandwich structures was given in [13]. This classification, in addition to the synphasic and antiphasic forms described and thoroughly studied in the literature, includes a mixed FSL of the external layers realized in zones of the moment stress-strain state (SSS) of the layer package as a whole.…”

“…To pose the problems for studying such FSLs, the corresponding linearized stability equations based on the Kirchhoff--Love hypotheses and the filler model adopted in [5,6] (the linear law of variation of displacement components over the thickness) were also deduced in [13]. The main distinction of the equations derived in this study from the known ones is that they take into account moment precritical SSS expressed by the inequality Ti;~ {lln~ the ~: T/j t ,, where T.,j ' ' are the tangential forces in the load-carrying layers.…”