Significant research is ongoing in the world to meet the needs of social and environmental crisis by harnessing wind and solar energy at high altitudes. One such approach is the use of an inflatable High Altitude Aerial Platform (HAAP). In the presented work, such periodically supported beam-like structures are analyzed using various mathematical models primarily modeling them as an equivalent beam using one-dimensional theories. The Euler-Bernoulli Theory (EBT) has been widely used for high aspect ratio beams, whereas the First Order Shear Deformation Theory (FSDT), or the Timoshenko beam theory, considers transverse shear effects and hence is superior in modeling low aspect ratio beams. First, an Isogeometric Analysis (IGA) is conducted using both FSDT and EBT to predict thermal buckling of periodically supported composite beams. Isogeometric analysis overcomes the limitations of the Gibbs phenomenon at discontinuities for a periodically supported beam using a higher order textit{k}-refinement. Next, an Integral Equation Approach (IEA) is implemented using EBT to obtain natural frequencies and buckling loads of periodically supported non-prismatic beams. Ill-conditioning errors were alleviated using admissible orthogonal Chebychev polynomials to obtain higher modes. We also present the prediction of the onset of flutter instability for metal plate and inflatable wing shaped foam test articles analyzed using finite element analysis (FEA). FEA updating based on modal testing and by conducting a geometrically nonlinear analysis resulted in a good agreement against the experiment tests. Furthermore, a nonlinear co-rotational large displacement/rotation FEA including the effects of the pressure as a follower forces was implemented to predict deformations of an inflatable structures. The developed FEA based tool namely Structural Analysis of Inflatables using FEA (SAIF) was compared with the experiments and available literature. It is concluded that the validity of the developed tool depends on the flexibility of the beam, which further depends upon the length of the beam and the bending rigidity of the beam. Inflatable structures analyzed with materials with high value of the Young's modulus and low to medium slenderness ratio tend to perform better against the experimental data. This is attributed to the presence of wrinkling and/or the Brazier effect (ovalling of the cross section) for flexible beams. The presented work has applications in programmable buckling, uncertainty quantification, and design of futuristic HAAP models to help face the upcoming environmental crises and meet the societal needs. / Doctor of Philosophy / In the future, developed countries are projected to face an increase in renewable energy demands due to environmental crises and increasing societal needs for energy due to urbanization. Wind energy, a renewable source, has received increasing attention. Wind farms require large land space and offshore wind energy harvesting is prone to unstable environments. Crosswind kite power is one of the promising and emerging fields where one can harvest energy from the wind farm inaccessible and apparently endless winds at high altitudes. In this dissertation, we present analysis and experiments on investigating complex structures, such as inflatable high altitude aerial platforms (HAAP) by using various mathematical models, primarily modeling them as an equivalent beam using one-dimensional theories. We investigate the effects of internal pressure on such structures, which unlike many other types of applied loads, follow the direction of the deflections. When supported on multiple supports, these structures are more efficient in terms of increased payload capacity due to a better distribution of loads, despite the increased weight penalty. To name a few, there are direct applications of periodic supports in design of bridges and railway sleepers. To avoid violent vibrations or failure, we also investigate the effect of multiple supports on the so-called natural frequency, vibration frequency under absence of applied loads, and buckling loads, instabilities under compression, of such beam-like structures. The presented work will aid in the design of futuristic HAAP models to help face the upcoming environmental crises and meet the energy demands of society due to urbanization.