scholarly journals NUMERICAL ANALYSIS OF CIRCULAR PLATES ON AN ELASTIC BASE WITH VARIABLE BED COEFFICIENT

2020 ◽  
pp. 66-75
Author(s):  
Yu.S. Krutii ◽  
◽  
M.G. Surianinov ◽  
M.M. Soroka ◽  
G.S. Karnauhova ◽  
...  
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Circular Plate ◽  
Elastic Foundation ◽  
Elastic Base ◽  
Variable Coefficients ◽  
Transverse Load ◽  
Decimal Point ◽  
Round Plate ◽  
Significant Digit

Abstract. The paper presents the results of a study of the stress-strain state of a circular plate of constant cylindrical stiffness, which lies on a variable elastic foundation and is under the influence of a continuously distributed transverse load. Twelve variants of calculation are considered ‒ six for a steel round plate and six more ‒ for a concrete round plate under two conditions of fixing and three different laws of variation of the bed coefficient. To solve the problem, the finite element method implemented in the LIRA-SAPR software package is used. It is noted that in the case when the bedding coefficient is a variable value depending on the coordinate in which the foundation settlement is determined, the analytical approach leads to the need to solve the corresponding differential equations with variable coefficients. Therefore, calculations of circular and annular plates lying on a variable elastic foundation by means of analytical solutions of differential equations are extremely rare in scientific periodicals and are of a private nature. An effective method for the analytical solution of differential equations with variable coefficients for a number of problems in mechanics was proposed by one of the authors of the article, however, the application of the method to the calculation of a circular plate on an elastic foundation with a variable bed coefficient requires verification, therefore, here we consider the features of the finite element analysis of such a plate under different boundary conditions and different laws of variation of the bed coefficient. In all versions, the results completely coincide with the known results of bending of slabs that do not have an elastic base and in the case when this base exists and its resistance is constant. The discrepancy here is very insignificant ‒ in the third significant digit after the decimal point for deflection when hinged and in the second for moments. In case of rigid clamping, the deflections and moments also differ from the corresponding values of the known solutions in the second significant digit after the decimal point.

scholarly journals A hybrid analytical-numerical solution for a circular pile under lateral load in multilayered soil

2020 ◽  
Vol 14 (1) ◽  
pp. 1-14
Author(s):  
Nghiem Xuan Hien
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Numerical Solution ◽  
Elastic Foundation ◽  
Three Dimensional ◽  
Bending Moment ◽  
Lateral Load ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

A hybrid analytical-numerical solution is proposed to solve the problem of a laterally loaded pile with a circular cross-section in multilayered soils. In the pile-soil model, the lateral load is located at the pile head including both lateral force and bending moment. The single pile is considered as a beam on elastic foundation while shear beams model the soil column below the pile toe. The differential equations governing pile deflections are derived based on the energy principles and variational approaches. The differential equations are solved iteratively by using the finite element method that provides results of pile deflection, rotation angle, shear force, and bending moment along the pile and equivalent stiffness of the pile-soil system. The modulus reduction equation is also developed to match the proposed results well to the three-dimensional finite element analyses. Several examples are conducted to validate the proposed method by comparing the analysis results with those of existing analytical solutions, the three-dimensional finite element solutions. Keywords: beam on elastic foundation; finite element method; pile; energy principle; lateral load.

scholarly journals ANALYTICAL AND NUMERICAL STUDIES OF THE STRESS-STRAIN STATE OF ROUND PLATES ON AN ELASTIC BASE WITH A VARIABLE BED COEFFICIENT

2020 ◽  
Author(s):  
Krutii Yurii ◽  
Surianinov Mykola ◽  
Soroka Mykola ◽  
Karnauhova Ganna
Keyword(s):  
Strain State ◽  
Elastic Base ◽  
Variable Coefficients ◽  
The Finite Element Method ◽  
Round Plate ◽  
Stress Strain ◽  
The Third ◽  
Stress Strain State ◽  
Numerical Studies ◽  
Elastic Resistance

The results of the study of the stress-strain state of a circular plate of constant cylindrical stiffness lying on an elastic foundation with a variable coefficient of elastic resistance are presented. Eight calculation options are considered − four each for a concrete round slab and for a steel round plate − under two conditions of fastening (hinged and rigid along the entire contour) and two laws of variation of the bed coefficient (according to the linear law and according to the law of the concave parabola). To solve the problem, the authors applied a general analytical method for solving differential equations with variable coefficients. The finite element method is used to verify the results. Comparison shows that the results coincide very well in deflections, differing in the third or fourth decimal places, and somewhat worse − in moments.

Submarine Pipeline Analysis With an Elastic Foundation by the Finite Element Method

1977 ◽  
Vol 99 (2) ◽  
pp. 480-484 ◽  
Author(s):  
W. F. Schmidt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Elastic Foundation ◽  
Nonlinear Differential Equations ◽  
Ocean Floor ◽  
Interface Condition ◽  
Submarine Pipeline ◽  
The Finite Element Method ◽  
Element Method

This paper presents a procedure for solving the nonlinear differential equations of bending for pipelines suspended between a lay barge and the ocean floor using the finite-element method. In order to eliminate the usual difficulty of determining the suspended length, a discontinuous foundation modulus is introduced into the formulation to account for the interface condition where the pipe lifts off the ocean floor. Examples are presented to illustrate the effectiveness, efficiency, and flexibility of the procedure, and it is concluded that the procedure should provide a useful tool enabling easy analysis of various schemes for pipelaying.

LATERAL VIBRATIONS OF BEAMS ON AN ELASTIC BASE AT CHANGING THE SUPPORTING CONDITIONS

2020 ◽  
Vol 91 (5) ◽  
pp. 70-76
Author(s):  
E.V. LEONTIEV ◽  
◽  
Keyword(s):  
Dynamic Behavior ◽  
Elastic Foundation ◽  
Dynamic Problem ◽  
Static Problem ◽  
Elastic Base ◽  
Design Model ◽  
Lateral Vibrations ◽  
Internal Forces ◽  
Vibration Loads ◽  
The Right

The paper considers the system "beam - elastic foundation", in which a beam with free edges was at first on a solid elastic foundation, but when a defect suddenly forms in the foundation under the right side of the beam, part of foundation was removed from design model. As a result of calculations performed by the method of initial parameters, the displacements and internal forces for the static problem are determined. The dynamic problem of determining the forces and displacements was solved, taking into account the three vibration loads F (t) = F sinγt applied at arbitrary points d when the conditions for supporting the right side of the beam on an elastic foundation were changed, the values of the dynamics coefficients were determined. Conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the influence of vibration loads in the case of a change in the conditions of bearing on an elastic foundation.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

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