Novel Integration Technique for Meshfree Methods.

摘要

Meshfree methods provide an alternative approach to the finite element method (FEM) for solving a variety of engineering problems. The robustness of these methods depends on the ability to precisely evaluate the integrands that are much more complicated and have to be integrated over complex geometrical domains. In this study, two techniques are proposed to alleviate these issues: a mapping technique by which complex domains can be mapped to simpler shapes and integrands over these domains, and also can be evaluated with greater accuracy, as well as an adaptive integration procedure where integration points are added in several levels or sets to existing integration points. A relative error value can be set as desired, so that when the difference of the final results between two levels is smaller, the integration procedure can be stopped. In this way, computational expense is decreased. These techniques can be applied to all types of meshfree methods that require domain integration. Results for various engineering problems by meshfree methods using the proposed techniques are obtained and compared to analytical values. The acquired data shows a close correlation to the analytical values, which proves the viability of these new suggested techniques.