This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

The use of composite materials has vastly increased in recent years. Great interest is therefore developed in the damage detection of composites using non- destructive test methods. Several approaches have been applied to obtain information about the existence and location of the faults. This paper used the vibration response of a composite plate to detect and localize delamination defect based on the modal analysis. Experiments are conducted to validate the developed model. A two-dimensional finite element model for multi-layered composites with internal delamination is established. FEM program are built for plates under different boundary conditions. Natural frequencies and modal displacements of the intact and damaged

The present investigation focuses on the response of simply supported reinforced concrete rectangular-section beams with multiple openings of different sizes, numbers, and geometrical configurations. The advantages of the reinforcement concrete beams with multiple opening are mainly, practical benefit including decreasing the floor heights due to passage of the utilities through the beam rather than the passage beneath it, and constructional benefit that includes the reduction of the self-weight of structure resulting due to the reduction of the dead load that achieves economic design. To optimize beam self-weight with its ultimate resistance capacity, ten reinforced concrete beams having a length, width, and depth of 2700, 100, and

The present work is concerned with the investigation of the behavior and ultimate capacity of axially loaded reinforced concrete columns in presence of transverse openings under axial load plus uniaxial bending. The experimental program includes testing of twenty reinforced concrete columns (150 × 150 × 700 mm) under concentric and eccentric load. Parameters considered include opening size, load eccentricity and influence of the direction of load eccentricity with respect to the longitudinal axis of the opening. Experimental results are discussed based on load – lateral mid height deflection curves, load – longitudinal shortening behavior, ultimate load and failure modes. It is found that when the direction of load

The polymeric hydrogels composed of poly vinyl alcohol (m.wt 72000) and glutaraldehyde(5%,8% and 10%) , have been thermally prepared for the purpose of studying their swelling and drug release behavior . The swelling ratio was measured for all the hydrogel samples at 37°C, in three different media pH (1.2, 4.7 and 6.8) as a function of time. The results show that the maximum swelling ratios were arranged as follows :pH =6.8 > pH =4.7 > pH =1.2 hydrogels cross linked PVA showed a typical pH responsive behavior such as high pH has maximum swelling while low pH shows minimum swelling.

In this research, nanofibers have been prepared by using an electrospinning method. Three types of polymer (PVA, VC, PMMA) have been used with different concentration. The applied voltage and the gap length were changed. It was observed that VC is the best polymer than the other types of polymers.

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result. 

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.