Technische Mechanik

On a virtual element formulation for trusses and beams

“…It is convenient to introduce a matrix formulation in order to shorten notation. This leads to the second derivative of w π w π = 2a 3 + 6a 4 x + 12a 5 x 2 = B (4) π (x) â…”

“…The definitions in (68) and (71) together with yield the matrix form of the projection of the ansatz function and its second derivative w π = N (4) π (x) P ( 4) w e and w π = B (4) π (x) B (4) w e (83)…”

“…Thus, many analytical and numerical simulation schemes were developed over the last century that can predict the displacements, deflections and normal, shear forces and bending moments in these structural members. Classical truss and beam models are described in any textbook on engineering mechanics, see, e.g., [6] and [4]. These models are based on kinematical assumptions which relate for beams to the names of Euler and Bernoulli for beams neglecting shear deformation.…”

“…] T G B(4) 24l e −3l2 e −60l e 168 24l e 192 −36l e −360 −24l e −3l 2 e −36l e 9l 2 e 60l e −360 −60l e −360 60l e 720…”

Simulation models investigating the dynamic characteristics of shock isolators

“…The shock mount (SM), the wire cable isolator with its specified design length d 0 = 0.135 m, is located in between the testing mass (traverse) M = 3.449 kg with the coordinate z 1 and the shock table with z 2 , respectively. Thus, it is advantageous to consider the relative displacement d = z 1 − z 2 − d 0 and its acceleration d = z1 − z2 for the mechanical model [6]. The dynamic force balance normalized by M can be written as…”