Analysis of beams on elastic foundations using Green's functions

IF 0.3 4区工程技术 Q4 ENGINEERING, MULTIDISCIPLINARY

Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria Pub Date : 2021-06-29 DOI:10.23967/j.rimni.2021.06.002

J. C. Molina-Villegas, Jorge Eliecer Ballesteros Ortega, Andrés Toro

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引用次数: 1

Abstract

Beams on elastic foundation are basic elements within structural analysis, which are used to model foundation beams, foundation piles, retaining walls, and more complex structures that include some of these elements. For their analysis, the finite element method is usually used [1], which produces an approximate solution of the problem; and the Green's function stiffness method [2], which produces an exact solution. This article presents a methodology 100% based on the use of Green function's (response to a unit point force), to obtain the exact response of beams on elastic foundation. The main advantage of this formulation is its computational low cost compared to the aforementioned alternatives, and even for a large number of problems, it can be expressed only by means of sums and integrals, which can be easily performed numerically. Also, a great variety of Green function's for finite and infinite beams on elastic foundations with different boundary conditions are also presented, as well as some examples with the implementation of the proposed methodology.

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弹性基础上梁的格林函数分析

弹性地基上的梁是结构分析中的基本元素，用于对基础梁、基础桩、挡土墙以及包括其中一些元素的更复杂结构进行建模。对于它们的分析，通常使用有限元方法[1]，该方法产生问题的近似解；以及格林函数刚度法[2]，该方法产生精确解。本文提出了一种100%基于格林函数（对单位点力的响应）的方法，以获得弹性地基上梁的精确响应。与上述替代方案相比，该公式的主要优点是计算成本低，即使对于大量问题，它也只能通过求和和和积分来表示，这可以很容易地在数值上执行。此外，还介绍了不同边界条件下弹性地基上有限梁和无限梁的各种格林函数，以及该方法的一些实施实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria 工程技术-工程：综合

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： International Journal of Numerical Methods for Calculation and Design in Engineering (RIMNI) contributes to the spread of theoretical advances and practical applications of numerical methods in engineering and other applied sciences. RIMNI publishes articles written in Spanish, Portuguese and English. The scope of the journal includes mathematical and numerical models of engineering problems, development and application of numerical methods, advances in software, computer design innovations, educational aspects of numerical methods, etc. RIMNI is an essential source of information for scientifics and engineers in numerical methods theory and applications. RIMNI contributes to the interdisciplinar exchange and thus shortens the distance between theoretical developments and practical applications.