SUMMARYIn this paper, a meshfree co-rotational formulation for two-dimensional continua is proposed. In a co-rotational formulation, the motion of a body is separated into rigid motion and strain producing deformation. Traditionally, this has been done in the setting of finite elements for beams and shell type elements. In the present work every node in a meshfree discretized domain has its own corotating coordinate system. Three key ingredients are established in order to apply the co-rotational formulation: (i) the relationship between global and local variables, (ii) the angle of rotation of a typical co-rotating coordinate system, and (iii) a variationally consistent tangent stiffness matrix.An algorithm for the co-rotational formulation based on load control is provided. Maximum-entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations. Numerical examples are presented to demonstrate the validity of the meshfree co-rotational formulation.
As an advanced modern engineering tool, the Finite Element Method (FEM) has been widely adopted in current undergraduate engineering curricula, especially in the discipline of mechanical engineering. However, the usage of FEM as a tool integrated into other fundamental engineering classes, such as statics and dynamics, fluid and thermal, and mechanics of materials, is not as common as one might suppose. Including, this present-day engineering tool is proposed to assist the teaching of deformation concepts in mechanics of materials. Due to the inherent complexity of FEM, a small finite element analysis (FEA) program, mini-FEA, developed by Professor Paul S. Steif at Carnegie Mellon University about fifteen years ago, is used to illustrate the concepts and quickly show how it works. For complex geometry, ANSYS Mechanical APDL programs were created by the instructor so that the requirements of student interaction with the program are minimal, and to keep their focus on deformation concepts. The mini-FEA allows the instructor to provide a quick illustration of deformation concepts as well as the basic steps in implementing FEM. The concepts of deformation mechanics are then demonstrated by graphical illustrations from both FEM and the traditional photoelasticity method. The purpose of this paper is to study the effectiveness of integrating FEM and discover how FEM further enhances students' learning in comparison with the traditionally used photoelasticity method. From the survey feedback, the effectiveness of the FEM model in enhancing student learning is clearly seen. Assessment of this approach and results of teaching strategies are presented.
The feasibility of using meshfree methods in nonlinear structural analysis is explored in an attempt to establish a new paradigm in structural engineering computation. A blended finite element and meshfree Galerkin approximation scheme is adopted to solve the inelastic response of plane frames. In the proposed method, moving least squares shape functions represent the displacement field, a plane stress approximation of the two-dimensional domain simulates beam bending, J2 plasticity characterizes material behavior and stabilized nodal integration yields the discrete equations. The particular case of steel frames composed of wide flange sections is investigated, though the concepts introduced can be extended to other structural materials and systems.Results of numerical simulations are compared with analytical solutions, finite element simulations and experimental data to validate the methodology. The findings indicate that meshfree methods offer an alternative approach with enhanced capabilities for nonlinear structural analysis. The proposed method can be integrated with finite elements so that a structural system is composed of mesh-free regions and finite-element regions to facilitate simulations of large-scale systems.
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