STRENGTH OF SHIPS’ GRILLAGES UNDER LATERAL LOAD AND IN-PLANE COMPRESSION

2021 ◽  
Vol 156 (A3) ◽  
Author(s):  
A Z Lokshin ◽  
V G Mishkevich ◽  
L D Ivanov
Keyword(s):  
Differential Equations ◽  
Elastic Foundation ◽  
Lateral Load ◽  
Simultaneous Action ◽  
Longitudinal Compression ◽  
Compression Load ◽  
Reaction Forces ◽  
Plane Compression ◽  
Rigid Supports ◽  
Euler Force

The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation. Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.

Strength of Ships’ Grillages Under Lateral Load and In-Plane Compression

2014 ◽  
Vol 156 (A3) ◽  
Keyword(s):  
Differential Equations ◽  
Elastic Foundation ◽  
Lateral Load ◽  
Simultaneous Action ◽  
Longitudinal Compression ◽  
Compression Load ◽  
Reaction Forces ◽  
Plane Compression ◽  
Rigid Supports ◽  
Euler Force

The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation. Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.

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.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

scholarly journals Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

Algorithms ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Nizam Ghawadri ◽  
Norazak Senu ◽  
Firas Adel Fawzi ◽  
Fudziah Ismail ◽  
Zarina Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Foundation ◽  
Fourth Order ◽  
Sixth Order ◽  
Test Problems ◽  
Type Method ◽  
Ill Posed ◽  
Runge Kutta ◽  
Fifth Order

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.

Development and Testing of Nano-Clay Composites for Pressure Pad Application

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
M.S. Vijaykumar ◽  
R. Saravanan ◽  
K. Rajasekar ◽  
N.V. Dhandapani
Keyword(s):  
Weight Ratio ◽  
Epoxy Composites ◽  
Launch Vehicles ◽  
Test Results ◽  
Compression Load ◽  
Ground Pressure ◽  
Loose Soil ◽  
Reverse Loading ◽  
Nano Clay ◽  
Reaction Forces

Pressure pads are used in mobile cranes and launch vehicles to distribute the reaction forces uniformly on the soil. In mobile cranes these pressure pads made on alloy steel and permanently fixed below the elephant foot through ball and socket joint. Launch vehicles are used to carry and outrigger the missiles in operating field or war field. Load distribution during the outrigger will be challenging in uneven ground surfaces and loose soils. Pressure pads add the flexibility in outriggering the missiles even in a loose soil with ground pressure of 4kg/cm2. Considering the place of application, detachable type pressure pads are used in launch vehicles. Aluminium alloy is preferred over the steel due to its less weight and easy handling. In this research study nano-clay epoxy composites are proposed as an alternate material for pressure pads of launch vehicles due to its high compression load and strength to weight ratio. The present study focused on the preparation of nano-clay epoxy composites and neat epoxy composites. The work further analyzed the deflection of composites during forward and reverse loading. Creep test was also conducted for a period of 4 hours. The test results revealed that the nano-clay composites were bearing more compressive strength with lesser weight than neat resin composites.

scholarly journals Transverse Motions of Bernoulli-euler Beam Resting on Elastic Foundation and under Two Concentrated Moving Loads

2020 ◽  
pp. 1-21
Author(s):  
A. Adedowole
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Elastic Foundation ◽  
Structural Members ◽  
Moving Loads ◽  
Structural Element ◽  
Euler Beam ◽  
Partial Differential ◽  
Order Four

Aims/Objectives: The aim is to obtain a closed form solutions of single-dimensional structural element of continuously supported by an elastic foundation. Thereafter, we classify the effects of the space d connecting the loads on the relevant partial differential equations governing the motion of the structural members. The study also analysis circumstances under which resonance occur in the dynamical systems involving structural members. Study Design: The single-dimensional structural element is a partial differential equation of order fourth order place on elastic Winkler foundation. The Bernoulli-Euler beam traversed by two moving loads. Place and Duration of Study: Department of Mathematical Sciences, Adekunle Ajasin University P.M.B. 01, Akungba-Akoko, Nigeria, between May 2019 and September 2019. Methodology: The principal equation of the single -dimensional beam model is governing by partial differential equation of the order four. For the single -dimensional beam problem, the solution techniques are based on the Fourier sine transformation. The governing partial differential equation of the order four was reduced to sequence of second order ordinary differential equations.

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