Mixed meshless local Petrov–Galerkin collocation method for modeling of material discontinuity

Jalušić, Boris; Sorić, Jurica; Jarak, Tomislav

doi:10.1007/s00466-016-1327-6

Cited by 11 publications

(19 citation statements)

References 29 publications

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“…Hence, the stiffness matrix can be solved directly and all the system equations are satisfied strictly. Besides, the proposed method remains high efficiency as the meshless local Petrov‐Galerkin collocation method (MLPGCM) for only the equations of the boundary nodes are modified. In addition, it is clear that no second derivatives of the shape functions are needed as the mixed scheme is used, which is a great advantage of the proposed method when compared with other MDCMs …”

Section: Mixed Dof Collocation Methods For Heterogeneous Structuresmentioning

confidence: 99%

“…In the first example, a heterogeneous plate that is the same as the plate in the work of Jalušić et al under a uniaxial linear continuous load at the right end is analyzed, as shown in Figure . The total length of the plate is 2 L =2 unit, and the height is H =1 unit.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The parameter k is set to 5 for the linear basis and 9 for the second‐order basis with r scale =1.15 for linear basis and r scale =1.05 for second‐order basis. For comparison, a MLPGCM with the same interpolation parameters is also provided. In the present study, only the discretizations with uniform nodal distributions are employed.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In another word, the present method remains the same efficiency as the MLPGCM. It should be mentioned that the MLPGCM used here for comparison purposes is recognized as a very efficient meshless implementation for modeling the material discontinuity, and it even outperforms the FEM for some problems …”

Section: Numerical Examplesmentioning

confidence: 99%

“…Lagrange multipliers are used to enforce the continuity of the displacements on the interface boundary. This simple model is used frequently in other methods …”

Section: Introductionmentioning

confidence: 99%

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A mixed DOF collocation method for elastic problems in heterogeneous structure

Mao

2019

Numerical Meth Engineering

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Summary In this paper, a collocation method with mixed degrees of freedom (DOFs) is proposed for heterogeneous structures. Local tractions of the outer and interface boundaries are introduced as DOFs in the mixed collocation scheme. Then, the equilibrium equations of all the nodes and the outer boundary conditions are discretized and assembled into the global stiffness matrix. A local force equilibrium equation for modeling the stress discontinuity through the interface is developed and added into the global stiffness matrix as well. With those contributions, a statically determined stiffness matrix is obtained. Numerical examples show that the present method is superior to the classical mixed collocation method in the heterogeneous structure because it improves the accuracy and the convergence and remains the efficiency. Besides, almost constant convergence rates of displacements and stresses are found in all the examples, even for three‐dimensional problems.

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Section: Mixed Dof Collocation Methods For Heterogeneous Structuresmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“…Lagrange multipliers are used to enforce the continuity of the displacements on the interface boundary. This simple model is used frequently in other methods …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations