The formulation and computer implementation of element-free Galerkin method for Euler-Bernoulli beam theory

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to digital@library.tamu.edu, referencing the URI of the item.Includes bibliographical references (leaf 76).Issued also on microfiche from Lange Micrographics.Element-free Galerkin (EFG) method is used to solve second and fourth-order one-dimesional problems. Moving least square (MLS) approximation is used to generate shape functions for the EFG model. MLS method is discussed in detail along with its key components: a polynomial basis, a set of coefficients and a weight function. Cubic and quartic weight functions are presented along with their derivatives. Numerical results for MLS shape functions and their derivatives are also presented. Stability issues and effects of boundaries on the shape of MLS functions are discussed. The EFG formulation of a fourth-order Euler-Bernoulli beam problem is presented. Essential boundary conditions are enforced using the Lagrange multiplier method. Weak form has been developed for the beam problem and MLS approximation has been used to discretize the problem. A general strategy for computer implementation is presented followed by detailed insight into the program EFGBEAM, which has been developed to find solutions to Euler-Bernoulli beam problems. A sample Euler-Bernoulli beam problem is solved using EFGBEAM and numerical results are presented