M 30mm Consider the below given Euler Bernoulli beam on an elastic foundation under the distributed...

 

Transcribed Image Text:

M 30mm Consider the below given Euler Bernoulli beam on an elastic foundation under the distributed upward linearly varying load of f=500 x [N] while the elasticity modulus is changing as E=70*(1+x/2) GPa (i.e., functionaly graded material). Note that there is no axial load and cross-section is variable. Q E=210 GPa Elastic foundation, k-50N/mm² L=2m 50mm 4mm Element stiffness and mass matrices are given in the attachment by the equations (1.1.5) and (1.1.9) in the book of Vadim Komkov et al (Hint: you can delete the rows and columns corresponding to axial displacements as no axial deformation exists in your problem). By using the notations given on p. 48 of T.J.R. Hughes' book titled "The Finite Element Method" do the following: 1) Present the strong form of the problem including the tip force and tip moment at x=0. 2) Obtain the weak form equations and the operators. 3) What is the consistent load vector for the first element? (Shape functions are given on p. 48 of T.J.R. Hughes' book) M 30mm Consider the below given Euler Bernoulli beam on an elastic foundation under the distributed upward linearly varying load of f=500 x [N] while the elasticity modulus is changing as E=70*(1+x/2) GPa (i.e., functionaly graded material). Note that there is no axial load and cross-section is variable. Q E=210 GPa Elastic foundation, k-50N/mm² L=2m 50mm 4mm Element stiffness and mass matrices are given in the attachment by the equations (1.1.5) and (1.1.9) in the book of Vadim Komkov et al (Hint: you can delete the rows and columns corresponding to axial displacements as no axial deformation exists in your problem). By using the notations given on p. 48 of T.J.R. Hughes' book titled "The Finite Element Method" do the following: 1) Present the strong form of the problem including the tip force and tip moment at x=0. 2) Obtain the weak form equations and the operators. 3) What is the consistent load vector for the first element? (Shape functions are given on p. 48 of T.J.R. Hughes' book)

Answer rating: 100% (QA)

Consider the stiffness matrix h 0 127 k Consider the mass matrix 140 0 M phl 420 0 hl ... View the full answer