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An improved reproducing kernel particle method for nearly incompressible finite elasticity. (English) Zbl 0973.74088
From the summary: A pressure projection method is introduced by locally projecting the pressure onto a lower-order space to reduce the number of independent discrete constraint equations. This approach relieves the over-constrained condition, and thus eliminates volumetric locking and pressure oscillation without employing large support size in reproducing kernel particle method (RKPM). The method is developed in a general framework of nearly incompressible finite elasticity, and therefore is also applicable to linear problems. To further reduce the computational cost, we develop a stabilized reduced integration method based on an assumed strain approach and on the gradient matrix associated with deformation gradient. The resulting stiffness matrix and force vector of RKPM are obtained explicitly without numerical integration.

74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
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