1. INTRODUCTION
The composite materials are the most popular for using in mechanical, aeronautical, civil and marine structure. Because of their high strength, small density, high stiffness and the controllability of property that is variable with the orientation and the thickness of the laminate. The behavior of structure that was constructed by composite material, mechanical behavior of rectangular laminate plate has drawn many attentions. Especially, the buckling phenomenon is the main focus which need to be considered for the competent and dependable design and secure procedure of the structural element. Due to the orthotropic characteristics of composite material, the analysis of homogeneous isotropic plate is normally easier than the composite laminate plate.
For the same material and the volume fraction of resin, the resistance of the composite laminate plate can be different due to the stacking sequence of fiber. It has several ways of fiber arrangement which found to be very popular. For crossply laminates and angleply laminate, the stacking sequence are [0/90]_{n} and [+θ/θ]_{2n}, respectively. Where, 2n is the total number of laminates. Furthermore, the symmetrical or antisymmetrical arrangement can make the stacking sequence become different (Reddy, 1997;Kollár and George, 2003). A semianalytical approach is developed by Shufrin and Eisenberger (2008) to analyze the buckling laminated composite plates. It demonstrated that a combination of biaxial compression, tension and shear modified the stability behaviour of angleply laminated plates. Besides, the buckling behaviour of the plate were changed by the presence of inplane restraints yields supplementary inplane forces.
Utilizing the finite element method (Avci et al., 2005), studied thermal buckling of laminate composite plate with hole for both clamped and simply supported at edges. To investigate the thermal buckling temperatures the eightnode Lagrangian finite element method was used. Thermal buckling of composite laminate plates with various types of boundary conditions was considered by Thangaratnam and Ramachandran (1989). Shiau et al (2010) demonstrated that α_{1}/α_{2} ratio and fiber orientation were the main factor responsible for the buckling of composite laminate plate. For simply support square angleply laminate plates, the stacking sequence with fiber orientated at 45^{o} obtained the highest critical buckling temperature. Ounis et al (2014) illustrated that the increasing of E_{1}/E_{2} ratio and α_{1}/α_{2} ratio can make the critical buckling temperature decrease. Also, the main factor affecting the buckling laminate composite plates were fiber orientation and boundary conditions. Shaterzadeh et al (2014) found the increment of critical thermal buckling temperature because the present of hole in the center of plate. Moreover, the critical thermal buckling temperature of symmetric composite plates were smaller than those of antisymmetric composite plates. Sim et al (2016) studied influence of stacking sequence and temperature on buckling resistance of GFRP infill panel. Simplified analysis on steel frame infill with FRP composite panel was investigated by Seo et al (2016). Buckling resistance of basalt fiber reinforced polymer infill panel subjected to elevated temperatures was studied by Sim et al (2017).
The objective of this study is to investigate the buckling resistance of basalt fiber laminate composite rectangular plates. To evaluate the buckling behavior of basalt fiber reinforced polymer (BFRP), The numerical approach was developed by using the finite element method. Also, buckling performance of thin composite plate subjected to combined loading was determined. Multiple parameters were studied, such as, boundary conditions, aspect ratio of plate dimension (a/b) and loading condition. Mechanical properties of BFRP were conducted with tensile and inplane shear test, by using domestically fabricated sample. The classical plate theory was utilized to analyze symmetrical laminate composite plate in this present paper.
2. EXPERIMENTAL PROCEDURE OF BFRP LAMINATE
2.1 Materials
In this study, the basalt fiber was supplied by Basalt Fiber Tech Company in Australia and the epoxy resin (EPOKUKDO YD128) was supplied by the Kukdo Chemical Company in South Korea. The specification properties of basalt fiber and epoxy resin used in this study were presented in Fig. 1. Furthermore, the mechanical properties of unidirectional basalt and epoxy such as: density, thickness, moisture content and viscosity were shown Table 1 and Table 2, respectively.
2.2 Sample preparation and test program
In this study, a series of experiments were performed to investigate the tensile performance (0° and 90° unidirectional) and inplane shear performance of the basalt fiber samples. Also, the tensile test with 0° unidirectional, tensile test with 90° unidirectional and inplane shear test samples were shown in Fig. 2(a), 2(b) and 2(c), respectively. The elastic modulus was determined from the linear portion of the stressstrain curve from both the tensile test and the inplane shear test (Modulus of elasticity). In order to fabricate the samples, five layers of basalt fiber was combined by hand layup and cured about two hours in the chamber with temperature 80°C. After taking out from the chamber, water jet cutter was used to cut the sample into specific sizes. The Universal Testing Machine (model ASTMHA) with capacity 100kN was used. Also, the strain gauge was installed at the central of the sample to measure the strain of the specimens was shown in Fig. 3. Finally, five samples were tested at each level of experiment and their average values were reported as the actual result.
Tensile tests of BFRP were conducted according to ASTM (D 3039/D 3039M  00), the tensile test samples were prepared according to the dimension shown in Table 3. The tensile test specimens were pulled with a strain rate of 0.01/min. Also, inplane shear test of BFRP were accomplished as per ASTM (D 4255/D 4255M  01). The specimen for this test has the following dimension: length 154mm, width 58mm, 3 holes along the length in both sides with diameter 10mm and the gap between each hole along the length were 51mm and along the width is 58mm. The inplane shear test was followed a standard strain rate of 0.01/min.
2.3 Test results
Fig. 4(a) demonstrated the stressstrain curves for tensile test (0° unidirectional). It was observed that the curve increased in a linear form. Thus, when the strain increased, the stress also increased. Fig. 4(b) showed the curve of stressstrain for tensile test (90° unidirectional). Also, it was found that the characteristics of the curve is similar to bilinear. The curves showed two distinct zones, divided at the strain of 0.0035. It increased quickly in strain from 0 to 0.0035. Conversely, for strain greater than 0.0035, this rapid increment was reduced. Fig. 4(c) showed the stressstrain for inplane shear test. It was found that this graph followed the exponential form. When strain between 0 to 0.03 the graph increases rapidly. In contrast, it increased slightly for strain greater than 0.03. The elastic modulus and shear modulus of elasticity was determined according to ASTM D 3039/D 3039M00 and D4255/D 4255M01, respectively.
Table 4 summarized the average results that were obtained from the graph above. Also, these results were used as input to calculate the buckling resistance.
3. VARIATION FORMULATION FOR STABILITY OF COMPOSITE LAMINATE PLATES
3.1 Theory of Composite Laminate Plates
Thin symmetrically rectangular laminated composite plates with dimensions a and b that is subjected to combined loading was studied. The geometry of plate and external force were illustrated in Fig. 5. The xy plane parallel to the middle plane of the plate and the zaxis is perpendicular to the middle plane.
Based on the classical Kirchhoff’s plate theory, the displacement of laminate composite plate is given by:
Where, (u, υ, w) are the displacements components along the (x, y, z) coordinate axes, respectively, and (u_{0}, υ_{0}, w_{0}) are the displacement on the middle plane of the plate. The straindisplacement relations are defined in condition of the displacement as follows:
where, є_{1} and є_{2} represent the linear and nonlinear parts of the strain are written as:
The [A], [B] and [D] matrices are the stiffness matrices of the laminate, and [Q] is the stiffness matrix of the ply. Fig. 6
The total potential energy π_{p} of the laminate plate under combined load is equal to the sum of strain energy and external force. The total potential energy is:
Where, U is the strain energy, V represents the external force inplane load.
3.2 Finite Element Formulations
The composite plate was modeled by using a commercial program, MATLAB, to develop a structure physical model. The whole model was divided into 10x10 meshes for all cases. There are four nodes per element with three degrees of freedom at each node. Therefore, the simplified shape function was used in this present paper to analyze the buckling load of composite plates. Fig. 7
The virtual linear strain energy
Where,
$\begin{array}{l}K={\displaystyle \iint {B}^{T}DBdxdy};\\ {K}^{D}={\displaystyle \iint \left\{\frac{\partial {N}_{i}}{\partial x},\text{\hspace{0.17em}}\frac{\partial {N}_{i}}{\partial y}\right\}\left[\begin{array}{cc}1& {P}_{xy}/{P}_{x}\\ {P}_{xy}/{P}_{x}& {P}_{y}/{P}_{x}\end{array}\right]\left\{\begin{array}{c}\frac{\partial {N}_{j}}{\partial x}\\ \frac{\partial {N}_{j}}{\partial y}\end{array}\right\}dxdy}\end{array}$
Where, K is the global stiffness matrix, K^{D} is the geometric matrix, P_{x} is the buckling loading and N is the shape function. The vector d is the ith buckling mode. Thus, buckling loads can be received by resolving the eigenvalue problem in Eq. (11). Fig. 8
3.3 Boundary conditions
Two types of boundary conditions were used, as the following:
Four edges clamped support (CCCC):
Four edges simply support (SSSS):
4. RESULTS AND DISCUSSIONS
The thickness of composite plates h = 2mm and a/h = 100 were studied. The parameters consider in this study are the following:

Stacking sequence: [45_{2}/45_{2}/0_{12}/45_{2}/45_{2}]

Aspect ratios of plate dimension (a/b) : 0.5, 1.0, 1.5, 2.0, and 2.5

Boundary conditions: simply support and clamped support

P_{y}/P_{x} ratio: 0.2, 0.4, 0.6, 0.8 and 1.0
where, P_{y} is applied force in y direction and P_{x} is applied force in x direction.
Fig. 9 illustrated the relationship between nondimensional buckling load and aspect ratio (a/b) from 0.5 to 2.5 with different ratio of (P_{y}/P_{x}) from 0.2 to 1.0. Moreover, the plate edges were considered simply support. Result of biaxial loading was shown in Fig. 9(a) and combined biaxial and shear loading was shown in Fig. 9(b). While the aspect ratio (a/b) between 0.5 and 1.0, it was found that the nondimensional buckling load decreased quickly for all (P_{y}/P_{x}) ratio cases, which decreasing around 58%. Alternatively, when the aspect ratio was between 1.0 and 2.5, it only slightly decreased. Thus, it meant that the bigger the aspect ratio was, the smaller the percentage decreased. Furthermore, it could be seen that the smaller (P_{y}/P_{x}) ratio was, the bigger the nondimensional buckling load was for both Fig. 9(a) and 9(b).
Fig. 10 showed the relationship between nondimensional buckling load and aspect ratio (a/b) from 0.5 to 2.5 in different ratio of (P_{y}/P_{x}) from 0.2 to 1.0. However, the plate edges had clamped support. It was observed that Fig. 10 had the same trend as Fig. 9 for both cases (a) and (b). According to Fig. 9 and 10, it was shown that while combined biaxial and shear load were applied, the percentage decrease of nondimensional buckling load was less than 4% when compare to applied only biaxial load. In conclusion, the inplane shear loading had a little effect on the nondimensional buckling load.
Fig. 11 illustrated the relationship between nondimensional buckling load and aspect ratio (a/b) from 0.5 to 2.5 in different ratio of P_{y}/P_{xy} from 0.2 to 1.0. The plate edges were supported by simply support and clamped support. Fig. 11(a) and 11(b) shown buckling resistance of laminate composite plates that subjected to combined biaxial and shear loading, respectively. For both simply support and clamped support with the aspect ratio of 0.5 to 1.0, it was found that the nondimensional buckling load decreased rapidly. Alternatively, it slightly decreased, when the aspect ratio was between 1.0 to 2.5. Moreover, for aspect ratio equal to 0.5, it was demonstrated that the smaller P_{y}/P_{xy} ratio was, the bigger the nondimensional buckling load became. While the aspect ratio getting bigger, in case of P_{y}/P_{xy} equal to 0.6, 0.8 and 1.0 the nondimensional buckling load had similar value for both simply support and clamped support. Therefore, it was concluded that if the aspect ratio were getting bigger, the P_{y}/P_{xy} ratio 0.6, 0.8 and 1.0, had very insignificant effect on nondimensional buckling load.
5. CONCLUSIONS
In this study, the buckling resistance of basalt fiber laminate composite rectangular plates subjected to combined loading was presented. Various parameters, like, aspect ratio (a/b), boundary condition and loading condition were investigated. The buckling behavior of basalt fiber reinforced polymer (BFRP) was evaluated with numerical approach by using the finite element method (FEM). The mechanical properties of BFRP were obtained under tensile and inplane shear test, by using domestically fabricated sample. The results could be summarized as follows:

For the cases of biaxial, combined biaxial and shear loading, when the aspect ratio was 0.5 and 1.0, the nondimensional buckling load decreased quickly. Alternatively, it decreased slightly, when aspect ratio was 1 to 2.5.

The smaller the (P_{y}/P_{x}) ratio was, the bigger the nondimensional buckling load became. This was true for both simply support and clamped support.

The adding inplane shear loading to existing axial loading, it could be seen that the decrement in nondimensional load is minuscule, about 4%.