By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fac...

Arbitrary Lagrangian Eulerian methods are well suited to modelling high speed compressible multimaterial flow problems in complex geometry. In this talk three stage ALE schemes will be considered, which are typically used for practical calculations of multimaterial flows. These three stages are: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, ...

In this talk, we present a trust region method for solving equality constrained optimization problems, which is motivated by the famous augmented Lagrangian function. It is different from standard augmented Lagrangian methods where the augmented Lagrangian function is minimized at each iteration. This method, for fixed Lagrange multiplier and penalty parameters, tries to minimize an approximate...

Unsaturated periporomechanics is a strong nonlocal poromechanics based on peridynamic state and effective force concept. In the previous periporomechnics total Lagrangian formulation adopted for solid skeleton of porous media. this article as new contribution we formulate implement an updated unsaturated framework modeling extreme large deformation in soils under drained condition, e.g., soil c...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

In this paper, an Arbitrary Lagrangian-Eulerian (ALE) method is addressed to solve dynamic problems involving large deformation. This ALE method is based upon the operator split technique in which the material displacements and mesh displacements are uncoupled. Special issues such as time-stepping, mesh refinement, dynamic equilibrium checks and remapping of state variables are briefly explaine...

A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options. At each timestep a set of one dimensional partial integral differential equations (PIDEs) is solved and the solution of each PIDE is updated using semi-Lagrangian timestepping. Crank-Nicolson and second order backward differencing timestepping schemes are studied. Monotonicity and stability results ...