n static analysis, there is no effect of mass (inertia) or of damping. In d ynamic analysis, nodal forces associated with mass/inertia and damping are included.
Static analysis is done using an implicit solver in LS-D!". Dynamic analysis can #e done via the e$plicit solver or the implicit solver.
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In nonlinear implicit analysis, solution of each step re%uires a series of trial solutions (iterations) to esta#lish e%uili#rium within a certain tolerance. In e$plicit analysis, no iteration is re%uired as the nodal accelerations are solved directly.
&he time step in e$plicit analysis must #e less than the 'ourrant time step (time it taes a sound wave to travel across an element). Implicit transient analysis has no inherent limit on the sie of the time step. "s such, implicit time steps are generally several orders of magnitude larger than e$plicit time steps.
Implicit analysis re%uires a numerical solver to invert the stiffness matri$ matri$ once or even several times over the course of a load/time step. &his matri$ inversion is an e$pensive operation, especially for large models. *$plicit doesn+t re%uire this step.
*$plicit analysis handles nonlinearities with relative ease as compared to implicit analysis. &his would include treatment of contact and material nonlinearities.
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In e$plicit dynamic analysis, nodal accelerations are solved directly (not iteratively) as the inverse of the diagonal mass matri$ times the net nodal force vector where net nodal force includes contri#utions from e$terior sources (#ody forces, applied pressure, contact, etc.), element stress, damping, #ul viscosity, and hourglass control. nce accelerations are nown at time n, velocities are calculated at time n/, and displacements at time n. 0rom displacements comes strain. 0rom strain comes stress. "nd "nd the cycle is repeated.
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1. Preliminary comments regarding the incremental nature of Explicit and Implicit Analysis A geometric and/or material nonlinear analysis requires incremental load (or displacement) steps. At the end of each increment the structure geometry changes and possibly the material is nonlinear or the material has yielded. Each of these things geometry change or material change may then need to be considered as you update your stiffness matrix for the next increment in the analysis. !. Explicit An Explicit "E# analysis does the incremental procedure and at the end of each increment updates the stiffness matrix based on geometry changes (if applicable) and material changes (if applicable). $hen a ne% stiffness matrix is constructed and the next increment of load (or displacement) is applied to the system. In this type of analysis the hope is that if the increments are small enough the results %ill be accurate. &ne problem %ith this method is that you do need many small increments for good accuracy and it is time consuming. If the number of increments are not sufficient the solution tends to drift from the correct solution. "uthermore this type of analysis cannot sol'e some problems. nless it is quite sophisticated it %ill not successfully do cyclic loading and %ill not handle
problems of snap through or snap bac. Perhaps most importantly this method does not enforce equilibrium of the internal structure forces %ith the externally applied loads. *. Implicit An Implicit "E# analysis is the same as Explicit %ith the addition that after each increment the analysis does +e%ton,-aphson iterations to enforce equilibrium of the internal structure forces %ith the externally applied loads. $he equilibirium is usually enforced to some user specified tolerance. o this is the primary difference bet%een the t%o types of anlysis Implicit uses +e%ton,-aphson iterations to enforce equilibrium. $his type of analysis tends to be more accurate and can tae some%hat bigger increment steps. Also this type of analysis can handle problems better such as cyclic loading snap through and snap bac so long as sophisticated control methods such as arc length control or generalied displacement control are used. &ne dra% bac of the method is that during the +e%ton,-aphson iterations one must update and reconstruct the stiffness matrix for each iteration. $his can be computationally costly. (As a result there are other techniques that try to a'oid this cost by using #odified +e%ton,-aphson methods.) If done correctly the +e%ton,-aphson iterations %ill ha'e a quadratic rate of con'ergence %hich is 'ery desireable. A suggestion. If you0d lie to learn further about these t%o techniques it %ould be instructi'e for you to use both techniques and compare on the same problem. Explicit can be done by simply turning off +e%ton,-aphson iterations in an Implicit routine or by setting the equilibrium tolerance to a large number in an implicit routine. As to the question of %hich method to use the ans%er is that it depends. $he type of analysis that is sufficient for your needs %ill depend on the type of problem that you are trying to sol'e. &ften times since dynamic analyses are computationally intensi'e they are done %ith the explicit method. o%e'er for static problems no% days it is becoming more common to do the full Implicit type of analysis. +onlinear analysis taes lots of experience and a careful understanding of %hat you %ant to accomplish and also a careful understanding of the anlaysis capabilities of the soft%are you are trying to use. As I mentioned I ha'e %ored %ith the abo'e methods of analysis in graduate school and no% a little about it ho%e'er I %ould be happy for others here at i#echanica %ho ha'e more experience than me to gi'e their thoughts on this as %ell. It is indeed a 'ery big topic that is difficult to co'er in 2ust a brief blog. 3ou should consider looing at 4risfield0s boo 'olume 1 for additional information. Also loo at the follo%ing location for nonlinear fem informationhttp://www.colorado.edu/engineering/CAS/courses.d/NFEM.d/Home.html
