I. Yu. Babich

The Three-Dimensional Theory of Stability of Fibrous and Laminated Materials

An analysis is made of the results of investigations into the internal and surface instability of fibrous and laminated composites within the framework of the piecewise-homogeneous model and the equations of the three-dimensional linearized theory of stability. The possible buckling modes of the reinforcing elements in composites with either an elastic (polymeric) or elastoplastic (metallic) matrix are studied. The reliability domains of applied approximate design models are determined and some applications of results on fracture (due to structural instability) of unidirectional composites are presented

Stability of Composite Structural Members (Three-Dimensional Formulation)

The results of stability analysis of composite structural members in a three-dimensional formulation are expounded. The effect of specific properties of composites on the critical loads is studied for single- and three-layer structural members and the applicability limits of applied theories are established.

Stability and efficient design of cylindrical shells of metal composites subject to combination loading

A study is made of the stability of boron-aluminum shells under a combination of axial compression and uniform external pressure. An approximate theoretical model is constructed to describe the deformation of a layer of a fiber composite consisting of elastoplastic components. The model is used to derive the equations of state of multilayered shells reinforced by different schemes. The nonlinear equation describing the subcritical state is solved by the method of discrete orthogonalization with the use of stepped loading. The homogeneous problem is also solved by discrete orthogonalization. It is shown that shells can be efficiently designed for combination loading by plotting the envelope of the boundary curves for specific reinforcement schemes. The envelope is convex for elastic shells and is of variable curvature for elastoplastic shells.

THE STABILITY OF CYLINDRICAL AND CONIC SHELLS MADE OF COMPOSITE MATERIALS WITH AN ELASTOPLASTIC MATRIX

Studies in which problems on the stability of shells made of inelastically deformed composite materials are formulated and solved are generalized. Primary attention is focused on works that employ a structural approach to the description of the deformation of a fibrous composite consisting of elastoplastic components. The load for which the solution of the problem becomes ambiguous (bifurcation) is considered critical. Boroaluminum cylindrical and conic shells subject to external pressure, axial compression, and combined loading by surface and axial forces of different signs are analyzed for stability. The effect of boundary conditions and reinforcement on the critical loads is considered. The effect of temperature on shell stability beyond the elastic limits is investigated by an example of a cylindrical shell.

On the applicability of the relations of the cubic timoshenko-type theory of shells to the study of the postcritical behavior of rods

The question of whether the nonlinear Timoshenko-type theory of shells can be applied to the study of the initial postcritical behavior of a rod under compression is considered. The Koiter asymptotic theory in the Budyanskii form is used. The exact solution of the problem is obtained and a formula for the coefficient of postcritical behavior allowing for the effect of lateral-shear strains is derived. It is shown that the expressions (specified to within cubic terms) for lateral-shear strains and curvature permit us to use the nonlinear theory of shells to analyze the initial supercritical behavior of rods

Linearized problems for an incompressible body in the case of small strains

Linear ized problems of the theory of elast ici ty for a compress ib le body are investigated in [4]. Some problems of an incompress ib le body in the case of finite s t ra ins are studied in [1, 5, 7]. We will const ruct the solutions of three-dimensional static and dynamic equations in variat ions for a nonlinearly elastic incompress ib le body in the case of a homogeneous initial state for different var iants of equations [6] with small initial s t ra ins . The solutions are constructed in an invariant form by solving second-o rde r equations for an a rb i t r a ry form of the elast ic potential. The investigations are conducted in Lagrangian coordinates x i (i = 1, 2, 3) which pr io r to deformation coincide with rec tangular coordinates . The notations used are borrowed f rom [4]. Summation f rom 1 to 3 is done over all r ecur r ing indices; f rom 2 to 5 over indices k and t; summation is not done over index m .