An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses

Implementation and validation of a Herschel-Bulkley PFEM model in Kratos Multiphysics

L'objectiu d'aquest treball de final de màster és la implementació i validació, mitjançant exemples en la literatura, de la llei constitutiva de Herschel-Bulkley de la dinàmica de fluids mitjançant el mètode d'elements finits de partícules (PFEM). La base del treball és la formulació PFEM per a fluids Bingham implementada a la plataforma del codi obert Kratos Multiphysics. El model de Herschel-Bulkley relaciona el tensor de tensions tallant amb el tensor de velocitat de deformació tenint en compte el límit elàstic, que limita l'inici o el final del moviment del fluid; la viscositat del fluid, que és responsable de la resistència del fluid al moviment; i l'índex del fluid, un paràmetre que representa el nivell de no-linealitat del moviment. La llei de Herschel-Bulkley és validada amb problemes de referència de la literatura. Es duu a terme la convergència en l'espai i el temps, l'anàlisi de sensibilitat de les variables del model i les comparacions amb el model estàndard de Bingham. A més, s'aplica l'anomenada regularització de Papanastasiou per a evitar els inconvenients numèrics del model de Herschel-Bulkley. Tots els resultats son graficats al llarg del treball i es comparen amb referències numèriques i experimentals trobades en articles científics. Al llarg dels càlculs numèrics és possible calibrar una sèrie de paràmetres fonamentals per a les simulacions amb el model.El objetivo de este trabajo de final de máster es la implementación y validación, mediante ejemplos en la literatura, de la ley constitutiva de Herschel-Bulkley de la dinámica de fluidos mediante el método de elementos finitos de partículas (PFEM). La base del trabajo es la formulación PFEM para fluidos Bingham implementada en la plataforma de código abierto Kratos Multiphysics. El modelo de Herschel-Bulkley relaciona el tensor de tensiones cortante con el tensor de velocidad de deformación teniendo en cuenta el límite elástico, que limita el inicio o el final del movimiento del fluido; la viscosidad del fluido, que es responsable de la resistencia del fluido al movimiento; y el índice del fluido, un parámetro que representa el nivel de no linealidad del movimiento. La ley de Herschel-Bulkley se valida con problemas de referencia de la literatura. Se lleva a cabo la convergencia en el espacio y el tiempo, el análisis de sensibilidad de las variables del modelo y las comparaciones con el modelo estándar de Bingham. Además, se aplica la llamada regularización de Papanastasiou para evitar los inconvenientes numéricos del modelo de Herschel-Bulkley. Todos los resultados se grafican a lo largo del trabajo y se comparan con referencias numéricas y experimentales encontradas en artículos científicos. A lo largo de los cálculos numéricos es posible calibrar una serie de parámetros fundamentales para las simulaciones con el modelo.The objective of this master's thesis is the implementation and validation, by means of literature examples, of the Herschel-Bulkley constitutive law in fluid dynamics in a particle finite element method (PFEM). The basis of the work is the PFEM formulation for Bingham fluids implemented in the open-source platform Kratos Multiphysics. The Herschel-Bulkley model relates the shear stress tensor to the strain rate tensor taking into account the yield stress, which limits the beginning or the end of the fluid motion; the fluid viscosity, which is responsible for the fluid's resistance to motion; and the fluid index, a parameter representing the level of nonlinearity of the motion. The Herschel-Bulkley law is validated with benchmark problems from the literature. Convergence in space and time, sensitivity analysis of the model variables and comparisons with the standard Bingham model are carried out. In addition, the so-called Papanastasiou regularization is applied to avoid numerical drawbacks arisign from the Herschel-Bulkley model. All results are plotted throughout the paper and compared to both numerical and experimental references found in scientific articles. Throughout the numerical calculations it is possible to calibrate a series of fundamental parameters for simulations with the model

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology

Research in nonlinear structural and solid mechanics

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis