University Events

Description: EAS Doctoral Dissertation Defense by Soolmaz Khoshkalam


Date: Friday,December 13, 2024

Time: 9:00 a.m.

Topic: Potential of Mean Force-Based Lattice Element: Extension to Dynamic and Nonlinear Analysis of Structures

Location: LIB 314

Abstract:

The potential-of-mean-force (PMF) approach to the lattice element method (LEM) has recently been adapted to model the response of structural systems. LEM relies on lattice discretization of the domain via a set of particles that interact through prescribed potential functions, representing the mechanical properties of members. The approach offers unique advantages, including robustness to discontinuity and failure without the need for mesh refinement. The overall goal of this research is two-fold: (i) extend the quasi-static PMF-based LEM to model the dynamic behavior of structures (ii) blend the quasi-static PMF-based LEM with Force Analogy method for nonlinear analysis. Such developments provide a means for simulating nonlinear response and failure under dynamic loading that is the nature of most natural hazards and extreme conditions. To accomplish the first goal, integration methods from Molecular Dynamics (MD) are used to estimate of the trajectory of particles in the Lattice Element Method (LEM) and to simulate the dynamic response with a focus on structural (or building) systems. More specifically Verlet-Velocity method is used to estimate the location and momentum of each particle at every time step. To assure accuracy and the numerical stability, we also explore implicit integration techniques such as Hilber-Hughes-Taylor method and midpoint method. Noting that the rotational degrees of freedom have minimal contribution to the kinetic energy of the system we develop an energy-based approach for condensation to reduce the computational cost. Our approach relies on the Euler-Lagrange equations and manifests itself in the form of minimum potential energy theorem for mass-less degrees of freedom. To address another critical aspect of dynamic simulation, the mass matrix, we adopt an energy-based approach and utilize the kinetic energy of the lattice elements to maintain consistency with the kinetic energy of their continuous counterparts. To achieve the second goal, we incorporate the nonlinear behavior of materials under various actions, including bending, torsion, and axial forces, through the introduction of novel potential functions inspired by the Force Analogy Method. These potential functions are calibrated using section properties that represent the nonlinear stress-strain responses of materials, such as nonlinear moment-curvature relationships. The utility of the proposed framework and its and accuracy are validated through its application in quasi-static linear and nonlinear simulations of large-scale buildings subjected to different loading conditions.


ADVISOR(S):

Dr. Mazdak Tootkaboni, Dept of Civil and Environmental Engineering (Advisor) (mtootkaboni@umassd.edu)

Dr. Arghavan Louhghalam, Dept. of Civil and Environmental Engineering (Co-Advisor)
(Arghavan_Louhghalam@uml.edu)


COMMITTEE MEMBERS: Dr. Alfa Heryudono, Department of Mathematics and Dr. Zheng Chen, Department of Mathematics


NOTE: All EAS Students are ENCOURAGED to attend.