Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting

Bolat Duissenbekov,Baisbay Yerimbetov,Abduhalyk Tokmuratov,Nurlan Zhangabay,Zhenis Orazbayev,Zhumadilla Aldiyarov

doi:10.1515/cls-2020-0005

Bolat Duissenbekov, Baisbay Yerimbetov + Show 4 more

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https://doi.org/10.1515/cls-2020-0005

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Abstract

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables,i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.

Highlights

Various classes of materials and structures working under creep conditions are widely used in modern engineering
The study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations
The resultant equations were written in a differential form and the problem of solving these differential equations was reduced to the solving of the Cauchy problem

Summary

Introduction

Various classes of materials and structures working under creep conditions are widely used in modern engineering. An analysis of the obtained solutions of the system of integral equations showed the influence of the mechanical and geometric parameters of the shell under the action of the axial tensile force on the distribution of stresses and strains near the circular aperture. A semi-analytical solution of nonlinear equations was adopted using the Galerkin method [10] for a nonlinear stability analysis of biconcave multilayer composite shallow shells. Such a solution has yielded nonlinear dependences of the load distribution of the four radii of curvature of curved shells, which are compared and

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