Nonlinear Analysis And Optimal Design Of Reinforced Concrete Plates And Shells

determinedenchiladaUrban and Civil

Nov 25, 2013 (4 years and 6 months ago)


Ministry of Higher Education

Scientific Research

University of Babylon

College of Engineering

Department of Civil Engineering

Nonlinear Analysis And
Optimal Design Of Reinforced
Concrete Plates And Shells

A Thesis

Submitted To The College Of Engineering Of
Babylon University In Partial Fulfilment Of The
Requirements For The Degree Of Master Of
Science In Civil Engineering



Ali Abdul Hussein M. Al

(B.Sc. 2005)

Supervised By:


Mr. Abdul Ridha S

Dr. Nameer A. Alwash

April 2008


This research deals with the optimal design of reinforced concrete plate and
shell structures based on nonlinear finite element method. The eight
degenerated curved shell element is used in which five degrees of freedom are
specified at each nodal poi
nt, which are three displacements and two rotations of the

normal at the node.

A layered model is considered in the modelling of the reinforced
concrete behaviour and a perfect bond between the concrete and reinforcement has
been assumed.

The compressive b
ehaviour of the concrete has been modelled by
employing two approaches both elastic
strain hardening and elasti

perfectly plastic

approach. The yield condition is formulated in terms of the first stress and
second deviatoric stress invariants.

The motion of the subsequent loading surface is
controlled by the hardening rule that is extrapolated from the uniaxial stress
relationship given by a parabolic function.

The behaviour of cracked concrete has been modelled using a smeared fixed
ck approach, coupled with a tensile criterion to predict crack initiation. Gradual
bond deterioration with progressive cracking is simulated by means of a tension
stiffening model. A reduced shear modulus is employed in the crack

zone. The
behaviour of s
teel reinforcement is idealized by elastic
perfectly plastic relation with
linear strain hardening for tensile and compressive stresses.

The nonlinear equations
of equilibrium have been solved using an incremental
iterative technique operating
under load c
ontrol. Modified Newton
Raphson method has been employed. In this
method, the stiffness matrix is updated in the second iteration of each load increment.
A load convergence criterion is adopted in the present work. Various integration rules
(full, selectiv
e, reduced) have been used in the analysis of the application presented in
this study.

A nonlinear geometrical model based on the total Lagrangian approach
and taking into account


on Karman


For the structural optimization problem, which i
s dealt with as a constraint
nonlinear optimization, the so
called Modified Hooke and Jeeves method,



is employed by considering the total cost of the structure as the objective
function and the dimensions as the design variables with geometri
cal constraints.

For the analysis of reinforced concrete plates and shells, several examples are worked
out using the present finite element analysis and the results show good agreement
with experimental results and the difference at the range of (3%
%) for the
ultimate load. The results of optimization for reinforced concrete plates show that the

optimal cost occurs when using of minimum thickness of slab.


optimal cost for
reinforced concrete cylindrical shell occurs when the thickness and curvature of the
shell increases and shell angle decreases.