patran nastran学习第2节显式瞬态动态分析求解技术一般通过有限元方法解决.pdfVIP

EXPLICIT SOLUTION TECHINIQUE ◼ General Technique ◆ Problem in space solved by FEM methods ◆ Problem in time solved by explicit time integration ⚫ Many small time rements ◼ Implementation in MSC.Dytran ◆ Problem in space solved by: ⚫ Lagrange-Finite Element Technology ⚫ Euler-Finite Volume Technology ◆ Problem in time solved by: ⚫ Central difference integration Explicit Time Integration ◼ Very efficient for large nonlinear problems (cpu time reases only linearly with DOF) ◼ No need to assemble stiffness matrix or solve system of equations ◼ Cost per time step is very low ◼ Stable time step size is limited by Courant condition ◆ time for stress wave to traverse an element ◆ problem duration typically ranges from microseconds to tenths of seconds) ◼ Particularly well-suited to nonlinear, high-rate dynamic problems ◆ nonlinear contact/impact ◆ nonlinear materials ◆ finite strains/large deformations Implicit Time Integration ◼ I tes until convergence (equilibrium) reached for each time step ◼ Stiffness matrix is reformed/updated and inverted; requires a linear solver to invert K matrix ◼ Cost per time step is relatively very high particularly for nonlinear problems ◼ No inherent limit on time step size ◆ Can use relatively large time step ◆ May fail to converge if time step is too large ◼ Typically used in low-rate dynamic or quasi-static problems Explicit Time Integration ◼ Based on Central Difference Method of time integration ◼ Equation of motion evaluated at old time tn (undamped) Ma = P - F + H n n n n M = diagonal mass matrix P = external loads + body F = internal (stress divergence vector)