A minimalistic smart array class template

Hi,
I've writing a container class as a replacement for raw arrays; just
called it smart_array (bare with me if it's dumb), which has the
niceties of a vector, can be used for dynamic memory requirements and
cleans up itself safely. When I showed it to my friends for a review
and to point out flaws & possible bugs in some peculiar use case; they
said I could post it here to get it reviewed/constructively criticized
by many C++ stalwarts. So am presenting it here:

smart_array.h :

#include <vector>
#include <cassert>
#include <cstdarg>
using std::vector;

template <typename T, size_t N>
class smart_array
{
    vector < smart_array<T, N - 1> > vec;

public:
    explicit smart_array(vector <size_t> &dimensions)
    {
        assert(N == dimensions.size());

        vector <size_t>::iterator it = ++dimensions.begin();
        vector <size_t> dimensions_remaining(it, dimensions.end());

        smart_array <T, N - 1> temp_smart_array(dimensions_remaining);
        vec.assign(dimensions[0], temp_smart_array);
    }

    explicit smart_array(size_t dimension_1 = 1, ...)
    {
        static_assert(N > 0, "Error: smart_array expects 1 or more
dimension(s)");
        assert(dimension_1 > 1);

        va_list dim_list;
        vector <size_t> dimensions_remaining(N - 1);

        va_start(dim_list, dimension_1);
            for(size_t i = 0; i < N - 1; ++i)
            {
                size_t dimension_n = va_arg(dim_list, size_t);
                assert(dimension_n > 0);
                dimensions_remaining[i] = dimension_n;
            }
        va_end(dim_list);

        smart_array <T, N - 1> temp_smart_array(dimensions_remaining);
        vec.assign(dimension_1, temp_smart_array);
    }

    smart_array<T, N - 1>& operator[](size_t index)
    {
        assert(index < vec.size() && index >= 0);
        return vec[index];
    }

    size_t length() const
    {
        return vec.size();
    }
};

template<typename T>
class smart_array<T, 1>
{
    vector <T> vec;

public:
    explicit smart_array(vector <size_t> &dimension) :
vec(dimension[0])
    {
        assert(dimension[0] > 0);
    }

    explicit smart_array(size_t dimension_1 = 1) : vec(dimension_1)
    {
        assert(dimension_1 > 0);
    }

    T& operator[](size_t index)
    {
        assert(index < vec.size() && index >= 0);
        return vec[index];
    }

    size_t length()
    {
        return vec.size();
    }
};

------ End of smart_array.h ------

Sample Usage:

#include "smart_array.h"
#include <iostream>
using std::cout;
using std::endl;

int main()
{
    // testing 1 dimension
    smart_array <int, 1> x(3);
    x[0] = 0, x[1] = 1, x[2] = 2;
    cout << "x.length(): " << x.length() << endl;

    // testing 2 dimensions
    smart_array <float, 2> y(2, 3);
    y[0][0] = y[0][1] = y[0][2] = 0;
    y[1][0] = y[1][1] = y[1][2] = 1;
    cout << "y.length(): " << y.length() << endl;
    cout << "y[0].length(): " << y[0].length() << endl;

    // testing 3 dimensions
    smart_array <char, 3> z(2, 4, 5);
    cout << "z.length(): " << z.length() << endl;
    cout << "z[0].length(): " << z[0].length() << endl;
    cout << "z[0][0].length(): " << z[0][0].length() << endl;
    z[0][0][4] = 'c'; cout << z[0][0][4] << endl;

    // testing 4 dimensions
    smart_array <bool, 4> r(2, 3, 4, 5);
    cout << "z.length(): " << r.length() << endl;
    cout << "z[0].length(): " << r[0].length() << endl;
    cout << "z[0][0].length(): " << r[0][0].length() << endl;
    cout << "z[0][0][0].length(): " << r[0][0][0].length() << endl;

    // testing copy constructor
    smart_array <float, 2> copied_y(y);
    cout << "copied_y.length(): " << copied_y.length() << endl;
    cout << "copied_y[0].length(): " << copied_y[0].length() << endl;

    cout << copied_y[0][0] << "\t" << copied_y[1][0] << "\t" <<
copied_y[0][1] << "\t" <<
        copied_y[1][1] << "\t" << copied_y[0][2] << "\t" << copied_y[1]
[2] << endl;

    return 0;
}

Thanks for your time!

Regards
Sundaram