## Implicit Dynamic Solver 2

Version 1.0.1 (5.32 KB) by
Implicit dynamic solver using non-linear Newmark's method

Updated 19 May 2022

Implicit dynamic solver using non-linear Newmark's method with two examples file.
function Result=Newmark_Nonlinear(Elements,Material,Support,M,C,f,U_s,dU_s,ddU_s,fs,delta)
Input:
Elements: a structure containing Elements{i}.DOFs, Elements{i}.Material, and Elements{i}.Material_State
where Elements{i}.DOFs=[j k] means element i connect DOF j with k
Elements{i}.Material=m assign material m to element i
Elements{i}.Material_State.e initial material strain
Elements{i}.Material_State.s initial material stress
Elements{i}.Material_State.k initial material hardening
Material: a structure containing material properties for bilinear springs
where Material{m}.E Stiffness
Material{m}.f_y Stress beyond which the stiffness decreases
Material{m}.Ep Reduced stiffness
Support: a vector of support (Fixed) DOFs of size (1,nSupport)
M: mass matrix (n*n)
C: damping matrix (n*n)
f: external force matrix(n,N)
U_s: support displacement matrix (nSupport,N)
dU_s: support velocity matrix (nSupport,N)
ddU_s: support acceleration matrix (nSupport,N)
fs: sampling frequency
delta: convergance criterion for residual force
where n is the number of DOFs, and N is the length of data points of dynamic force
Output:
Result: is a structure consist of
Result.Displacement: Displacement (n,N)
Result.Velocity: Velocity (n,N)
Result.Acceleration: Acceleration (n,N)
Result.F_s: Support Force (nSupport,N)
References
Chopra, Anil K. "Dynamics of Structures. Theory and Applications to." Earthquake Engineering (2017).

### Cite As

Ayad Al-Rumaithi (2023). Implicit Dynamic Solver 2 (https://www.mathworks.com/matlabcentral/fileexchange/111695-implicit-dynamic-solver-2), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2022a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux