scholarly journals Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory

2015 ◽  
Vol 125 ◽  
pp. 575-585 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Lidiya Kurpa ◽  
Tatiana Shmatko
Keyword(s):  
Variable Thickness ◽  
Nonlinear Vibrations ◽  
Geometrically Nonlinear ◽  
Shallow Shells ◽  
Geometrically Nonlinear Vibrations ◽  
R Functions

THE SUPPORT BONDS RIGIDITY INFLUENCES ON THE CARRYING CAPACITY REDUCTION OF THE SHALLOW SHELLS ON A RECTANGULAR PLAN

2020 ◽  
Vol 92 (6) ◽  
pp. 3-12
Author(s):  
A.G. KOLESNIKOV ◽  
Keyword(s):  
Variable Thickness ◽  
Carrying Capacity ◽  
Geometric Nonlinearity ◽  
Progressive Collapse ◽  
Geometrically Nonlinear ◽  
Loss Of Stability ◽  
Shallow Shells ◽  
Capacity Reduction ◽  
Internal Forces ◽  
Hinged Support

Geometric nonlinearity shallow shells on a square and rectangular plan with constant and variable thickness are considered. Loss of stability of a structure due to a decrease in the rigidity of one of the support (transition from fixed support to hinged support) is considered. The Bubnov-Galerkin method is used to solve differential equations of shallow geometrically nonlinear shells. The Vlasov's beam functions are used for approximating. The use of dimensionless quantities makes it possible to repeat the calculations and obtain similar dependences. The graphs are given that make it possible to assess the reduction in the critical load in the shell at each stage of reducing the rigidity of the support and to predict the further behavior of the structure. Regularities of changes in internal forces for various types of structure support are shown. Conclusions are made about the necessary design solutions to prevent the progressive collapse of the shell due to a decrease in the rigidity of one of the supports.

Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments

2007 ◽  
Vol 306 (3-5) ◽  
pp. 580-600 ◽  
Author(s):  
Lidia Kurpa ◽  
Galina Pilgun ◽  
Marco Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Shallow Shells ◽  
Complex Boundary ◽  
R Functions
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