The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices whe...The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices when handling rotational degrees of freedom,leading to compromised performance in both time and frequency domains analyses.This study proposes a manifold-based mass lumping scheme that systematically resolves the inertia matrix formulas for rotational/torsional degrees of freedom.By reinterpreting the finite element mesh as a mathematical cover composed of overlapping patches,Hermitian interpolations for plate deflection are derived using partition of unity principles.The manifold-based mass matrix is constructed by integrating the virtual work of inertia forces over these patches,ensuring symmetry and positive definiteness.Numerical benchmarks demonstrate that the manifold-based mass lumping scheme performance can be comparable or better than the consistent mass scheme and other existing mass lumping schemes.This work establishes a unified theory for mass lumping in fourth order plate dynamics,proving that the widely used row-sum method is a special case of the manifold-based framework.The scheme resolves long-standing limitations in rotational/torsional inertia conservation and provides a foundation for extending rigorous mass lumping to 3D shell and nonlinear dynamic analyses.展开更多
The simulation of industry-scale reactive bulks is challenging due to the complex interaction between fluid and particles.The particles in the bulk and their interaction with the fluid flow can be described by combine...The simulation of industry-scale reactive bulks is challenging due to the complex interaction between fluid and particles.The particles in the bulk and their interaction with the fluid flow can be described by combined Discrete Element Method-Computational Fluid Dynamics(DEM-CFD)models.However,the computational cost of the Finite Volume(FV)methods deployed in these models can become prohibi-tively expensive,especially for high inner-particle resolution.Single particle Reduced Models(RMs)can be used to achieve both fast and accurate descriptions of the processes in each particle.As an example of bulk systems comprising heat and mass transfer,we compared FV and RM simulations for the drying of wood chips in a bulk reactor.A manifold-based nonlinear interpolation was applied to resolve changing boundary conditions for the RM.Our simulations showed that RMs provide accurate values for the thermodynamic state variables of the particles.Furthermore,the time required for the bulk simulation was reduced by 67%with the RMs.It is evident that simulations with high inner-particle resolution can be accelerated by RMs if manifold-based nonlinear interpolation is used to address changing boundary conditions.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.42107214 and 52130905)the Natural Science Foundation of Chongqing(No.CSTB2024NSCQMSX0740)the Henan Province Science and Technology Research Projects(No.252102220050).
文摘The vibration analysis of Kirchhoff plates requires robust mass lumping schemes to guarantee numerical stability and accuracy.However,existing methods fail to generate symmetric and positive definite mass matrices when handling rotational degrees of freedom,leading to compromised performance in both time and frequency domains analyses.This study proposes a manifold-based mass lumping scheme that systematically resolves the inertia matrix formulas for rotational/torsional degrees of freedom.By reinterpreting the finite element mesh as a mathematical cover composed of overlapping patches,Hermitian interpolations for plate deflection are derived using partition of unity principles.The manifold-based mass matrix is constructed by integrating the virtual work of inertia forces over these patches,ensuring symmetry and positive definiteness.Numerical benchmarks demonstrate that the manifold-based mass lumping scheme performance can be comparable or better than the consistent mass scheme and other existing mass lumping schemes.This work establishes a unified theory for mass lumping in fourth order plate dynamics,proving that the widely used row-sum method is a special case of the manifold-based framework.The scheme resolves long-standing limitations in rotational/torsional inertia conservation and provides a foundation for extending rigorous mass lumping to 3D shell and nonlinear dynamic analyses.
基金funded by the Deutsche For-schungsgemeinschaft(DFG,German Research Foundation)-Project-ID 422037413-TRR 287.Gefordert durch die Deutsche Forschungsgemeinschaft(DFG)-Projektnummer 422037413-TRR 287.
文摘The simulation of industry-scale reactive bulks is challenging due to the complex interaction between fluid and particles.The particles in the bulk and their interaction with the fluid flow can be described by combined Discrete Element Method-Computational Fluid Dynamics(DEM-CFD)models.However,the computational cost of the Finite Volume(FV)methods deployed in these models can become prohibi-tively expensive,especially for high inner-particle resolution.Single particle Reduced Models(RMs)can be used to achieve both fast and accurate descriptions of the processes in each particle.As an example of bulk systems comprising heat and mass transfer,we compared FV and RM simulations for the drying of wood chips in a bulk reactor.A manifold-based nonlinear interpolation was applied to resolve changing boundary conditions for the RM.Our simulations showed that RMs provide accurate values for the thermodynamic state variables of the particles.Furthermore,the time required for the bulk simulation was reduced by 67%with the RMs.It is evident that simulations with high inner-particle resolution can be accelerated by RMs if manifold-based nonlinear interpolation is used to address changing boundary conditions.
