Q2. What is the only unknown function to be approximated in the finite element implementation of the principle?
A strain field vector remains the only unknown function to be approximated in the finite element implementation of the principle.
Q3. What are the typical problems of the Timoshenko composite beam finite elements?
In the case of Timoshenko composite beam finite elements with an interlayer slip, the typical locking problems are shear and slip locking.
Q4. What is the objective of the present paper?
The second objective of the present paper is the incorporation of the transverse shear deformation into the two-layer composite beam theory with an interlayer slip.
Q5. What is the main advantage of using rigid shear connectors?
With the use of rigid shear connectors, a full shear connection and full composite action between the individual components can be achieved.
Q6. What is the geometric shape of the cross-section of each layer?
The geometric shape of the cross-section of each layer is assumed to be arbitrary but symmetric with respect to (x, z) plane and constant along its longitudinal axis x.
Q7. What is the main disadvantage of all these theories and their closed form analytical solutions?
The main disadvantage of all these elastic theories and their closed form analytical solutions is that they could be obtained only for problems with simple geometry, loading and boundary conditions.
Q8. What is the position vector of the material particles of the deformed configurations of layers a?
The position vectors of material particles of the deformed configurations of layers a and b in the plane of deformation (y = 0) are defined by vector-valued functionsRa(x, z) = ( x + ua(x) + z ϕa(x) ) Ex + ( z + wa(x) )
Q9. What are the common examples of multi-layered structures in civil engineering?
Classical cases of such structures in civil engineering are steel-concrete composite beams in buildings and bridges, wood-concrete floor systems, coupled shear walls, concrete beams externally reinforced with laminates, sandwich beams, and many more.
Q10. What is the main purpose of the interlayer-slip effect?
the inclusion of the interlayer-slip effect into multi-layered beam theory is essential for optimal design and accurate representation of the actual mechanical behaviour of multi-layered structures with partial interaction between the components.
Q11. What are the main advantages of multi-layered structures?
Multi-layered structures have been playing an increasingly important role in different areas of engineering practice, perhaps most notably in civil, automotive, aerospace and aeronautic technology.
Q12. What is the description of a composite beam?
As only a few finite elements are needed to describe a composite beam of a frame with great precision, the new finite element formulations is perfectly suited for practical calculations.
Q13. How can the authors reduce or completely eliminate locking?
It ispossible to reduce or completely eliminate locking by lowering the degree of interpolation functions for the slip or by introducing elements with larger numbers of degrees of freedom [18, 21].
Q14. What is the disadvantage of the interlayer-slip effect?
the full shear connection can hardly be materializied in practice and thus only an incomplete or partial interaction between the layers can be obtained and aninterlayer slip often develops.
Q15. How is the distribution of interlayer slip shown?
In order to show that the present finite elements are slip-locking-free, the distribution of interlayer slip along the span of a simply supported beam is shown for low (Fig. 3) and high (Fig. 4) connection stiffness.
Q16. What methods have been used to solve the problem of shear and membrane locking?
Among all those numerical methods, the majority of researchers have employed the displacement-based [16, 18], force-based [19] and mixed [18–22] finite element method.
Q17. What is the simplest way to define the eqs of layers?
The application of Eqs. (18–19) to the first and second derivative of Eq. (14) with respect to x, gives modified Eqs. (18–19) by which the rotations and pseudocurvatures of layers are constrained to each other.