Nonlinear vibrational and rotational analysis of microbeams in nanobiomaterials using Galerkin decomposition and differential transform methods

In this paper, a nonlinear vibrational and rotational analysis of microbeams in nanobiomaterials using Galerkin Decomposition (GDM) and Differential Transform Methods (DTM) is presented. The dependency of cell migration and growth on nanoscaffold porosity and pore size architecture in tissue regeneration is governed by a dynamic model for the nonlinear vibration and rotation of the microbeams of nanobiomaterials and represented by a set of nonlinear partial differential equations. The solutions of the governing model are obtained by applying GDM and DTM and good agreement is achieved with numerical Runge-Kutta method (RK4). From the results, it is observed that an increase in Duffing term resulted in the increase of the frequency of the micro-beam. An increase in the foundation term also resulted in a corresponding increase in the frequency of the system for both free and forced dynamic responses. This study will enhance the application of tissue engineering in the regeneration of damaged human body tissues.

The average method is much better than average

Operator splitting is a powerful method for the numerical investigation of complex time-dependent models, where the stationary (elliptic) part consists of a sum of several structurally simpler sub-operators. As an alternative to the classical splitting methods, a new splitting scheme is proposed here, the Average Method with sequential splitting. In this method, a decomposition of the original problem is sought in terms of commuting matrices. Wedemonstrate that third-order accuracy can be achieved with the Average Method. The computational performance of the method is investigated, yielding run times 1-2 orders of magnitude faster than traditional methods.

A comparative study of URANS, DDES and DES simulations of Jetstream 31 aircraft near the compressibility limit

This work presents a comparative study of Unsteady Reynolds–Averaged Navier–Stokes (URANS), Detached Eddy Simulations (DES) and Delayed Detached Eddy Simulations (DDES) turbulence modeling approaches by performing numerical investigation with the ANSYS-FLUENT software package on a full-scale model of the Jetstream 31 aircraft. The lift and drag coefficients obtained from different models are compared with flight test data, wind tunnel data and theoretical estimates. The different turbulence models are also compared with each other on the basis of pressure coefficient distributions and velocity fluctuations along various lines and sections of the aircraft. For the mesh and the conditions presented in this study, the DDES Spalart–Allmaras model gives the best overall results.

Methodology of model development in the applied sciences

The formulation and validation of mathematical models in the applied sciences are largely consistent with the methodology of scientific research programmes (MSRP), however an essential modification is necessary: The domain of calibration has to be defined. The ranking and systematic improvement of mathematical models based on objective criteria are described and illustrated by an example. The methodology outlined in this paper provides a framework for the evolutionary development of a large class of mathematical models.

Finding a weak solution of the heat diffusion differential equation for turbulent flow by Galerkin's variation method using p-version finite elements

The stochastic turbulence model developed by Professor Czibere provides a means of clarifying the flow conditions in pipes and of describing the heat evolution caused by shear stresses in the fluid. An important part of the theory is a consideration of the heat transfer-diffusion caused by heat generation. Most of the heat is generated around the pipe wall. One part of the heat enters its environment through the wall of the tube (heat transfer), the other part spreads in the form of diffusion in the liquid, increasing its temperature. The heat conduction differential equation related to the model contains the characteristics describing the turbulent flow, which decisively influence the resulting temperature field, appear. A weak solution of the boundary value problem is provided by Bubnov-Galerkin’s variational principle. The axially symmetric domain analyzed is discretized by a geometrically graded mesh of a high degree of p-version finite elements, this method is capable of describing substantial changes in the temperature gradient in the boundary layer. The novelty of this paper is the application of the p-version finite element method to the heat diffusion problem using Czibere’s turbulence model. Since the material properties depend on temperature, the problem is nonlinear, therefore its solution can be obtained by iteration. The temperature states of the pipes are analyzed for a variety of technical parameters, and useful suggestions are proposed for engineering designs.

Simulation of cellular structures with a coupled FEM-FCM approach based on CT data

The application of cellular structural materials provide new light-weight capabilities in many engineering fields. But the microstructure significantly influences the strength, the fatigue and fracture behavior as well as the life span of a structure made from cellular materials. The current paper illustrates the general idea how to take into account the cellular microstructure in the stress and strain analysis. The detailed geometry, including all discontinuities in the microstructure is available, for instance from measurements provided by the computed tomography (CT). The proposed simulation methodology is a combination of the finite element method (FEM) and the finite cell method (FCM). The FCM approach is applied in regions where discontinuities occur, avoiding a body-fitted mesh. As basis of the FEM-FCM coupling the commercial FEA package Abaqus is used. The theoretical background and the overall simulation workflow along with specific implementation details are discussed. Finally, academic benchmark problems are used to verify the developed coupling method.

Deformation of a cantilever curved beam with variable cross section

This paper deals with the determination of the displacements and stresses in a curved cantilever beam. The considered curved beam has circular centerline and the thickness of its cross section depends on the circumferential coordinate. The kinematics of Euler-Bernoulli beam theory are used. The curved elastic beam is fixed at one end and on the other end is subjected to concentrated moment and force; three different loading cases are considered. The paper gives analytical solutions for radial and circumferential displacements and cross-sectional rotation and circumferential stresses. The presented examples can be used as benchmark for the other types of solutions as given in this paper.

Vibration of an axially loaded heterogeneous pinned-pinned beam with an intermediate roller support

The present paper is devoted to the issue of what effect the axial load (compressive or tensile) has on the eigenfrequencies of a heterogeneous pinned-pinned beam with an intermediate roller support (called a PrsP beam). This problem is a three point boundary value problem (eigenvalue problem) associated with homogeneous boundary conditions. If the Green functions of the three point boundary value problem (BVP) are known the eigenvalue problem that provide the eigenfrequencies for the beam loaded axially can be transformed into an eigenvalue problem governed by a homogeneous Fredholm integral equation. The later eigenvalue problems can be reduced to an algebraic eigenvalue problem which then can be solved numerically by using an effective solution algorithm which is based on the boundary element method.

A steady-state heat conduction problem of a nonhomogeneous conical body

Numerous studies and textbooks deal with the steady-state thermal conduction of radially nonhomogeneous circular cylinder. In contrast, there are relatively few studies on the thermal conduction problems of conical solid bodies. This study is intended as a modest contribution to the solution of thermal conductance problems of nonhomogeneous conical bodies. A one-dimensional steady-state heat conduction in nonhomogeneous conical body is considered. The thermal conductivity of the hollow conical body in a suitable chosen spherical coordinate system depends on the polar angle but is independent of the radial coordinate and azimuthal angle coordinate. A functionally graded type of material inhomogeneity is considered. All results of the paper are based on Fourier’s theory of heat conduction in solid bodies.