difference between linear analysis and non-linear analysis?

Question

i need the clear explain on this terms with examples

Answer 1

Linear analysis has nothing to do with straight lines. It just says that if you have a system with a math function associated with it and have more than one input, the answer will be the sum of how the function operates on the inputs. The function can be a simple equation, an integral or a derivative among other things. A non linear system means that the inputs interact with another .... for example, the output depends on the product of the two inputs.

Linear analysis basically says that if you have two inputs, X and Y and two constants, a and b and a function F that;

F(aX+bY) = aF(X) + bF(Y)

Answer 2

Linear analysis refers to analyzing a system whose input/output characteristics are such that a signal only changes in amplitude and or phase from input to output of the system. Example: An amplifier (ideally only). Linear analysis such as Laplace equations are typically used.

Non-linear analysis refers to analyzing a system that changes it's input signals beyond just amplitude and phase. Example: diode rectifier. A sine wave is rectified - that is non linear. Non linear analysis techniques such as Harmonic Balance etc. are used on non linear systems.

Answer 3

Linear models use simple parameters and assume that the material is not plastically deformed. Non-linear models consist of stressing the material past its elastic capabilities. The stresses in the material then vary with the amount of deformation.{basic definition}. Nonlinearities can be caused by changes in geometry or be due to nonlinear material behavior. for ex:a bar distributed with axial load having constant young's modulus in linear fea.assumptions in linear fea cross-section of the bar does not change after loading. # The material is linear elastic, isotropic, and homogeneous. # The load is centric. # End-effects are not of interest to us. and the same bar with material constants varying from initial to final E,is non linear.

Answer 4

y = x > linear (straight graph)
y = x^2 > non-linear (curved graph)