Strength and stability of geometrically nonlinear orthotropic shell structures

• The technique of research strength and stability of orthotropic shells is proposed.
• The study of orthotropic shells must take into account geometric nonlinearity.
• The strength and stability of the shell structures must be considered together.
• The values of loads of strength loss and buckling of the certain shells are obtained.
• Before total loss of stability of thin shells occurs multiple local buckling.

The article presents a methodology for the study of shell structure strength and stability. The basis of the study is a geometrically nonlinear mathematical model, which takes into account the transverse shifts and orthotropy of material. The model is presented in dimensionless parameters in the form of the total energy potential functional and can be used for different types of shells of revolution.The model is studied by using an algorithm based on the Ritz method and the method of solution continuation according to the best parameter (MSCBP), which allows for obtaining the values of the upper and lower critical loads and examining the supercritical behavior of designs.In accordance with an algorithm, the computer program has been developed and a comprehensive study of the strength and stability of shallow shells (which are square in plane), cylindrical, and conical panels has been explored. The load loss of strength and buckling load values have been obtained, and their relationship to one another has been demonstrated.