Dissertations / Theses on the topic 'Structural analysis (Engineering) Mechanics, Applied'

Bio-structures owe their remarkable mechanical properties to their hierarchical geometrical arrangement as well as heterogeneous material properties. This dissertation presents an integrated, interdisciplinary approach that employs computational mechanics combined with flow network analysis to gain fundamental insights into the failure mechanisms of high performance, light-weight, structured composites by examining the stress flow patterns formed in the nascent stages of loading for the rostrum of the paddlefish. The data required for the flow network analysis was generated from the finite element analysis of the rostrum. The flow network was weighted based on the parameter of interest, which is stress in the current study. The changing kinematics of the structural system was provided as input to the algorithm that computes the minimum-cut of the flow network. The proposed approach was verified using two classical problems – three- and four-point bending of a simply-supported concrete beam. The current study also addresses the methodology used to prepare data in an appropriate format for a seamless transition from finite element binary database files to the abstract mathematical domain needed for the network flow analysis. A robust, platform-independent procedure was developed that efficiently handles the large datasets produced by the finite element simulations. Results from computational mechanics using Abaqus and complex network analysis are presented. The complex network strategy successfully identified failure mechanisms in the bio-structure by identifying strain localization in regions of tension, and buckling/crushing in regions of compression. The transdisciplinary strategy used in this study identified the failure mechanisms early, when the material was still in the linearly elastic regime, thereby tremendously reducing the computational time and cost as compared to running a finite element analysis to failure. This work also developed five proof-of-concept, bio-inspired models with varying lattice complexity based on the rostrum. Performance of these bio-inspired models was analyzed with respect to the stress and deformation. Numerical experiments were carried out on one of the bio-inspired model to demonstrate the application of newly developed similitude laws for blast loading. This research has laid the groundwork for an efficient design-test-build cycle for rapid prototyping of novel bio-inspired structures by using flow network analysis, finite element analysis, and similitude laws.

Methods for modeling structural failure with applications for fluid structure interaction (FSI) are developed in this work. Fracture as structural failure is modeled in this work by both the extended finite element method (XFEM) and element deletion. Both of these methods are used in simulations coupled with fluids modeled by computational fluid dynamics (CFD). The methods presented here allow the fluid to pass through the fractured areas of the structure without any prior knowledge of where fracture will occur. Fracture modeled by XFEM is compared to an experimental result as well as a test problem for two phase coupling. The element deletion results are compared with an XFEM test problem, showing the differences and similarities between the two methods.

A new method for modeling fracture is also proposed in this work. The new method combines XFEM and element deletion to provide a robust implementation of fracture modeling. This method integrates well into legacy codes that currently have element deletion functionality. The implementation allows for application by a wide variety of users that are familiar with element deletion in current analysis tools. The combined method can also be used in conjunction with the work done on fracture coupled with fluids, discussed in this work.

Structural failure via buckling is also examined in an FSI framework. A new algorithm is produced to allow for structural subcycling during the collapse of a pipe subjected to a hydrostatic load. The responses of both the structure and the fluid are compared to a non-subcycling case to determine the accuracy of the new algorithm.

Overall this work looks at multiple forms of structural failure induced by fluids modeled by CFD. The work extends what is currently possible in FSI simulations.

The focus of this work is to advance the theoretical and modeling techniques for the fields of hybrid simulation and multi-slider friction pendulum systems (MSFPs). Hybrid Simulation is a simulation technique involving the integration of a physical system and a computational system with the use of actuators and sensors. This method has a strong foundation in the experimental mechanics community where it has been used for many years. The hybrid simulation experiments are performed with the assumption of an accurate result as long as the main causes of error are reduced. However, the theoretical background on hybrid testing needs to be developed in order validate these findings using this technique. To achieve this objective, a model for hybrid simulation is developed and applied to three test cases: an Euler-Bernoulli beam, a nonlinear damped, driven pendulum, and a boom crane structure. Due to the complex dynamics that these three test cases exhibit, L² norms, Lyapunov exponents, and Lyapunov dimensions, as well as correlation exponents were utilized to analyze the error in hybrid simulation tests. From these three test cases it was found that hybrid simulations are highly dependent on the natural frequencies of the dynamical system as well as how and where the hybrid split is located. Thus, proper care must be taken when conducting a hybrid experiment in order to guarantee reliable results.

Multi-stage friction pendulum systems (MSFPs), such as the triple friction pendulum (TFP), are currently being developed as seismic isolators. However, all current analytical models are inadequate in modeling many facets of these devices. Either the model can only handle uni-directional ground motions while incorporating the kinetics of the TFP system, or the model ignores the kinetics and can handle bi-directional motion. And in all cases, the model is linearized to simplify the equations. The second part of this dissertation presents an all-in-one model that incorporates the full nonlinear kinetics of the TFP system, while allowing for bi-directional ground motion. In this way, the model presented here is the most complete single model currently available. It was found that the non-linear model can more accurately predict the experimental results for large displacements due to the nonlinear kinematics used to describe the system. The model is also able to successfully predict the experimental results for bi-directional ground motions.

The work presented in this dissertation describes a general algorithm and its Finite Element (FE) implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which the domain under analysis can be selectively discretized spatially and temporally, hence allowing the user to obtain a desired level of accuracy in critical regions whilst improving computational efficiency globally. The mathematical background for this approach is largely derived from the fundamental principles of Domain Decomposition Methods (DDM) and Lagrange Multipliers, used to obtain coupled equations of motion for distinct regions of a continuous domain. These methods when combined together systematically yield constraint forces that not only ensure conservation of energy, but also enforce continuity of field quantities across sub-domain interfaces. Multiple Grid (MG) coupling between conforming or non-conforming sub-domains is achieved in the form of linear multi-point constraints that are modeled using Mortar Finite Element Method (M-FEM); whereas coupled Multiple Time-scale (MT) equations are derived for the classical Newmark integration scheme and its constituent algorithms. A rigorous proof of stability is provided using Energy Method and necessary conditions for enforcing energy balance are discussed in reference with field variables that are selected to enforce sub-domain interface continuity. Fully discretized equations of motion for component sub-domains, augmented with an interface continuity condition are then solved using block elimination method and Crout factorization. A step-by-step solution approach, utilizing recursive black box sub-routines, is modeled in order to allow efficient implementation within existing finite element frameworks.

Proposed MGMT Method and corresponding solution algorithm is systematically implemented by using the finite element approach and programming in FORTRAN 90. Resulting in-house code - FEAPI (Finite Element Analysis Programming Interface) is capable of solving linear structural dynamics problems that are modeled using independently discretized sub-domains. Auxiliary sub-routines for defining pre simulation parameters and for viewing global/component sub-domain results are built into FEAPI and work in conjugation with GiD; a universal, adaptive and user-friendly pre and post-processor. Overall stability, numerical accuracy and computational efficiency of MGMT Method is evaluated and verified using a series of benchmark examples. Verification matrices take into consideration performance evaluation factors such as energy balance (at global and component-sub-domain levels), interface continuity, evolution/distribution of kinematic quantities and propagation of structural waves across connecting sub-domains. Assessment of computational efficiency is derived by comparing the size of respective FE problems (nodes, elements, number of equations, skyline storage requirements) and the required computation times (CPU solution time). Discussed examples highlight the greatest advantage of MGMT Method; which is significant gain in simulation speedups (at the cost of reasonably small errors).

This thesis demonstrates a new application of Groebner basis by finding an analytical solution to geometrically nonlinear axisymmetric isotropic circular plates. Because technology is becoming capable of creating materials that can perform materially in the linear elastic range while experiencing large deformation geometrically, more accurate models must be used to ensure the model will result in realistic representations of the structure. As a result, the governing equations have a highly nonlinear and coupled nature. Many of these nonlinear problems are solved numerically. Since analytic solutions are unavailable or limited to only a few simplified cases, their analysis has remained a challenging problem in the engineering community.

On the other hand, with the increasing computing capability in recent years, the application of Groebner basis can be seen in many areas of mathematics and science. However, its use in engineering mechanics has not been utilized to its full potential. The focus of this thesis is to introduce this methodology as a powerful and feasible tool in the analysis of geometrically nonlinear plate problems to find the closed form solutions for displacement, stress, moment, and transverse shearing force in the three cases defined in Chapter 4.

The procedure to determine the closed form solutions developed in the current study can be summarized as follows: 1) the von Kármán plate theory is used to generate nonlinear governing equations, 2) the method of minimum total potential energy combined with the Ritz methodology converts the governing equations into a system of nonlinear and coupled algebraic equations, 3) and Groebner Basis is employed to decouple the algebraic equations to find analytic solutions in terms of the material and geometric parameters of the plate. Maple 13 is used to compute the Groebner basis. Some examples of Maple worksheets and ANSYS log files for the current study are documented in the thesis.

The results of the present analysis indicate that nonlinear effects for the plates subjected to larger deformation are significant for predicting the deflections and stresses in the plates and necessary compared to those based on the linear assumptions. The analysis presented in the thesis further shows the potential of the Groebner basis methodology combined with the methods of Ritz, Galerkin, and similar approximation methods of weighted residuals which may provide a useful procedure of analysis to other nonlinear problems and a basis of preliminary design in engineering practice.