Based on meta-modeling, which allocates structural mechanics as mathematical approximation of con-tinuum mechanics, this paper proposes a conversion method from a solid element solution to a beam element solution. A key issue is the rigorousness of the proposed conversion method, since meta-modeling ensures that the most suitable beam element solution is the one that is close to the solid element solution by defining a distance between these solutions in a function space of continuum mechanics. Examples of applying the conversion method are presented. It is shown that the conversion method produces a more accurate beam element solution from a solid element solution, compared to an ordinary method. It is also shown that the conversion method is applicable to a practical problem of an actual large-scale tunnel structure.
Inspired by work of Payen et al.1),2), this paper seeks to make mechanical interpretation of nodal force, in order to more accurately evaluate stress field using linear element of finite element analysis. A new mechanical interpretation is presented for nodal forces, which is an abstract quantity with a rigorous mathematical definition. Use of Lagrangean and particle discretization scheme reveals that nodal force gives total force acting on middle plane of element. Based on the aforementioned interpretation, this paper proposes a method for more accurately evaluating stress field. Numerical experiments indicate that stress field of proposed method is smoother and accurate compared to ordinary element stress evaluation. Moreover, it is found that the error of J-integral, for a mode-I crack problem, is several times smaller when estimated with nodal force based stress evaluation.
Theoretical stability and error analysis on a Conforming Petrov-Galerkin Finite Element (CPGFE) scheme with the fitting technique for solving the Advection-Dispersion-Decay Equations (ADDEs) on connected graphs is performed. This paper is the first research paper that applies the concept of the discrete Green's function (DGF) to error analysis on a numerical scheme for the ADDEs on connected graphs. Firstly, the stability analysis shows that the scheme is unconditionally stable in space for steady problems and is stable in both space and time for unsteady problems if the temporal term is appropriately discretized with a lumping technique. Secondly, basic properties of the DGF on connected graphs, which provide key mathematical tools in the error analysis, are presented. The error analysis with the DGF reveals a direct relationship between the regularity conditions on the known functions and accuracy of the scheme, explicitly indicating that the accuracy of the scheme is strongly influenced by the accuracy of the discretized known functions. The error analysis also shows that the scheme is uniformly-convergent in the L∞-error norm with respect to the diffusivity, which cannot be achieved in the conventional numerical schemes. This unique and remarkable property is a significant advantage of the present CPGFE scheme over the conventional ones.
This paper studies the extension of particle discretization scheme (PDS) in order to improve finite element method implemented with this discretization scheme (PDS-FEM). Polynomials are included in the basis functions, while original PDS uses a characteristic function or zero-th order polynomial only. It is shown that including 1st order polynomials in PDS, the rate of the convergence reaches the value of 2 even for the derivative. 1st order polynomials are successfully included in PDS-FEM. A numerical experiment is carried out by applying 1st order PDS-FEM, and the improvement of the accuracy is discussed.
We examined aggregation rates of colloidal particles in a shear flow as a function of KCl (potassium chloride) concentration at different shear rates. The analysis was based on the trajectory analysis with non-linear Poisson-Boltzmann (PB) solution that calculates the double layer force between highly charged particles. The trajectory analysis here is performed without any adjustable parameters. The PB solution enables us to analyze the experimental data of orthokinetic aggregation of highly charged particles where linearized PB solution is not valid. It should be noted that the comparison of the calculation with the experimental data of aggregation rates in a simple shear flow in the presence of the double layer repulsion had never been attempted until we analyzed. The theoretical calculation with trajectory analysis qualitatively describes the experimental data. However, theoretical values of critical coagulation concentration (CCC) being a bending point of capture efficiencies plotted against the KCl concentration, and capture efficiencies in the presence of double layer force are not quantitatively consistent with experimental ones. These discrepancies might be caused by the additional forces and charge heterogeneity which are not included in the present calculation.
The failure of slope and levee triggered by heavy rainfall is a great threat to people's lives and properties, thus this research aimed at proposing a new numerical simulation tool and investigating the failure mechanism of slope and levee under heavy rainfall. The new Smoothed Particle Hydrodynamics (SPH) model with the coupling of three phases, water, soil and air, has been proposed based on the basic principles. Using the proposed SPH program, the rising and burst of air bubble in water was simulated to validate the application in fluid phase (water and air). After that, a conceptual slope model with different coefficients of permeability has been built and analyzed by the SPH model. The simulated infiltration showed that the proposed SPH model can simulate the interaction force between soil and water well. The model test of slope failure conducted before was simulated by the proposed SPH model with two cases, one without the effect of air phase and another one with the effect of air phase. The infiltration process, slope deformation and air behavior were revealed from the three-phase SPH simulations and the results proved that the proposed SPH model could be a useful tool to evaluate the stability of slope and levee under heavy rainfall.