A new and effective virtual-pulse (VIP) time integral methodology for computational dynamics: Theoretical developments, implementation aspects, and applicability for large-scale built-up structures

Predicting the transient behavior of systems is of practical importance in several areas of engineering and sciences. In practice, for the transient analysis of general built-up structures, analytical solutions are normally not feasible, while experiments are often either too expensive or impractical in many situations. As a consequence, numerical methods such as finite element methods are a viable alternative. Traditionally, direct time integration and mode superposition methods are the two most commonly used approaches. Using existing numerical approaches and modern computer environments, the engineering transient analysis of several large scale problems is still not feasible or may be cost prohibitive because of extensive computational efforts required. Hence, there is a pressing need for developing effective computational tools to meet the current and future demands in engineering analysis.; The objectives of the present research are to develop an effective VIrtual-Pulse (VIP) Time Integral Methodology via new perspectives for general structural dynamics and transient heat transfer problems and provide a sound theoretical foundation. The applicability to large scale general structures is a major concern. The proposed VIP methodology capitalizes on the advantages of both direct time integration and mode superposition methods and possess improved algorithmic characteristics and computational attributes. In comparison to existing methods, the VIP method has several attractive computational features such as: (1) explicit (with iteration for nonlinear situations) and unconditionally stable; (2) second-order accurate; (3) zero algorithmic damping and relative period error for linear dynamic systems, and no acceleration involved in computations; and (4) direct self-starting.; Based on the investigation of various elastic and elasto-plastic engineering structures/components presented in this work under different boundary, loading, and initial conditions, it is shown that the proposed Virtual-Pulse Time Integral Methodology is effective for both linear and nonlinear structural dynamics. It improves the convergence characteristics and can significantly reduce computational cost for prescribed accuracy levels in comparison to existing approaches. The methodology not only provides new perspectives and approach for developing effective computational tools, but also offers significant potential for the analysis of large scale engineering computations on modern computing environments.