Energy conservation error in the material point method for solid mechanics
Journal of Computational Physics
Concepts and Applications of Finite Element Analysis
Concepts and Applications of Finite Element Analysis
The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis
Finite Elements in Analysis and Design
Review: Meshless methods: A review and computer implementation aspects
Mathematics and Computers in Simulation
Mitigating kinematic locking in the material point method
Journal of Computational Physics
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This paper analyses different types of spatial interpolation for the material-point method. The interpolations include quadratic elements and cubic splines in addition to the standard linear shape functions usually applied. For the small-strain problem of a vibrating bar, the best results are obtained using quadratic elements. It is shown that for more complex problems, the use of partially negative shape functions is inconsistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations of field quantities. The properties of different interpolation functions are analysed using numerical examples, including the classical cantilevered beam problem.